Answer: 24

Prompt: What is the sum of the decimal digits of 3993?

Solution: Digits of 3993 sum to 24.


Answer: 12

Prompt: What is the sum of the decimal digits of 5034?

Solution: Digits of 5034 sum to 12.


Answer: 17

Prompt: What is the sum of the decimal digits of 2096?

Solution: Digits of 2096 sum to 17.


Answer: 18

Prompt: What is the sum of the decimal digits of 882?

Solution: Digits of 882 sum to 18.


Answer: 10

Prompt: What is the sum of the decimal digits of 4006?

Solution: Digits of 4006 sum to 10.


Answer: 30

Prompt: What is the sum of the decimal digits of 6978?

Solution: Digits of 6978 sum to 30.


Answer: 29

Prompt: What is the sum of the decimal digits of 7589?

Solution: Digits of 7589 sum to 29.


Answer: 13

Prompt: What is the sum of the decimal digits of 1129?

Solution: Digits of 1129 sum to 13.


Answer: 17

Prompt: What is the sum of the decimal digits of 1916?

Solution: Digits of 1916 sum to 17.


Answer: 27

Prompt: What is the sum of the decimal digits of 8289?

Solution: Digits of 8289 sum to 27.


Answer: 30

Prompt: What is the sum of the decimal digits of 9876?

Solution: Digits of 9876 sum to 30.


Answer: 26

Prompt: What is the sum of the decimal digits of 8882?

Solution: Digits of 8882 sum to 26.


Answer: 18

Prompt: What is the sum of the decimal digits of 369?

Solution: Digits of 369 sum to 18.


Answer: 820

Prompt: What is the 40th triangular number T_n = n(n+1)/2?


Answer: 276

Prompt: What is the 23th triangular number T_n = n(n+1)/2?


Answer: 153

Prompt: What is the 17th triangular number T_n = n(n+1)/2?


Answer: 351

Prompt: What is the 26th triangular number T_n = n(n+1)/2?


Answer: 630

Prompt: What is the 35th triangular number T_n = n(n+1)/2?


Answer: 36

Prompt: What is the 8th triangular number T_n = n(n+1)/2?


Answer: 465

Prompt: What is the 30th triangular number T_n = n(n+1)/2?


Answer: 595

Prompt: What is the 34th triangular number T_n = n(n+1)/2?


Answer: 190

Prompt: What is the 19th triangular number T_n = n(n+1)/2?


Answer: 91

Prompt: What is the 13th triangular number T_n = n(n+1)/2?


Answer: 496

Prompt: What is the 31th triangular number T_n = n(n+1)/2?


Answer: 78

Prompt: What is the 12th triangular number T_n = n(n+1)/2?


Answer: 45

Prompt: What is the 9th triangular number T_n = n(n+1)/2?


Answer: 163

Prompt: Write the positive integer 115 in base 8 (no prefix, lowercase if hex).

Solution: 115 in base 8 is 163 (check: int('163', 8)=115).


Answer: 1b

Prompt: Write the positive integer 27 in base 16 (no prefix, lowercase if hex).

Solution: 27 in base 16 is 1b (check: int('1b', 16)=27).


Answer: 50

Prompt: Write the positive integer 80 in base 16 (no prefix, lowercase if hex).

Solution: 80 in base 16 is 50 (check: int('50', 16)=80).


Answer: 24

Prompt: Write the positive integer 20 in base 8 (no prefix, lowercase if hex).

Solution: 20 in base 8 is 24 (check: int('24', 8)=20).


Answer: 41

Prompt: Write the positive integer 33 in base 8 (no prefix, lowercase if hex).

Solution: 33 in base 8 is 41 (check: int('41', 8)=33).


Answer: 4d

Prompt: Write the positive integer 77 in base 16 (no prefix, lowercase if hex).

Solution: 77 in base 16 is 4d (check: int('4d', 16)=77).


Answer: b8

Prompt: Write the positive integer 184 in base 16 (no prefix, lowercase if hex).

Solution: 184 in base 16 is b8 (check: int('b8', 16)=184).


Answer: 2a

Prompt: Write the positive integer 42 in base 16 (no prefix, lowercase if hex).

Solution: 42 in base 16 is 2a (check: int('2a', 16)=42).


Answer: 1100101

Prompt: Write the positive integer 101 in base 2 (no prefix, lowercase if hex).

Solution: 101 in base 2 is 1100101 (check: int('1100101', 2)=101).


Answer: 33

Prompt: Write the positive integer 27 in base 8 (no prefix, lowercase if hex).

Solution: 27 in base 8 is 33 (check: int('33', 8)=27).


Answer: 233

Prompt: Write the positive integer 155 in base 8 (no prefix, lowercase if hex).

Solution: 155 in base 8 is 233 (check: int('233', 8)=155).


Answer: 10110100

Prompt: Write the positive integer 180 in base 2 (no prefix, lowercase if hex).

Solution: 180 in base 2 is 10110100 (check: int('10110100', 2)=180).


Answer: 277

Prompt: Write the positive integer 191 in base 8 (no prefix, lowercase if hex).

Solution: 191 in base 8 is 277 (check: int('277', 8)=191).


Answer: 302

Prompt: Write the positive integer 194 in base 8 (no prefix, lowercase if hex).

Solution: 194 in base 8 is 302 (check: int('302', 8)=194).


Answer: 10110001

Prompt: Write the positive integer 177 in base 2 (no prefix, lowercase if hex).

Solution: 177 in base 2 is 10110001 (check: int('10110001', 2)=177).


Answer: -8

Prompt: Evaluate p(x)=-1x^3 + (-2)x^2 + (4)x + (-3) at x=-1.


Answer: -8

Prompt: Evaluate p(x)=2x^3 + (-3)x^2 + (0)x + (-3) at x=-1.


Answer: -11

Prompt: Evaluate p(x)=1x^3 + (3)x^2 + (4)x + (1) at x=-3.


Answer: 66

Prompt: Evaluate p(x)=2x^3 + (1)x^2 + (2)x + (-3) at x=3.


Answer: 2

Prompt: Evaluate p(x)=2x^3 + (1)x^2 + (-2)x + (2) at x=0.


Answer: -12

Prompt: Evaluate p(x)=3x^3 + (4)x^2 + (3)x + (2) at x=-2.


Answer: 151

Prompt: Evaluate p(x)=4x^3 + (4)x^2 + (2)x + (1) at x=3.


Answer: 2

Prompt: Evaluate p(x)=-2x^3 + (3)x^2 + (-2)x + (3) at x=1.


Answer: 28

Prompt: Evaluate p(x)=-1x^3 + (1)x^2 + (2)x + (-2) at x=-3.


Answer: 8

Prompt: Evaluate p(x)=2x^3 + (1)x^2 + (1)x + (4) at x=1.


Answer: 2

Prompt: Evaluate p(x)=3x^3 + (-1)x^2 + (4)x + (2) at x=0.


Answer: -9

Prompt: Evaluate p(x)=-3x^3 + (2)x^2 + (3)x + (1) at x=2.


Answer: 0

Prompt: Evaluate p(x)=-3x^3 + (-2)x^2 + (3)x + (2) at x=1.


Answer: 7

Prompt: Evaluate p(x)=-1x^3 + (-3)x^2 + (-1)x + (4) at x=-3.


Answer: 1

Prompt: Evaluate p(x)=-1x^3 + (-2)x^2 + (0)x + (2) at x=-1.


Answer: -1

Prompt: Evaluate p(x)=3x^3 + (-3)x^2 + (-1)x + (4) at x=-1.


Answer: 42

Prompt: y is inversely proportional to x. When x=7, y=18. What is y when x=3?

Solution: xy constant=126; y=126/3=42.


Answer: 10

Prompt: y is inversely proportional to x. When x=4, y=20. What is y when x=8?

Solution: xy constant=80; y=80/8=10.


Answer: 6

Prompt: y is inversely proportional to x. When x=3, y=8. What is y when x=4?

Solution: xy constant=24; y=24/4=6.


Answer: 3.125

Prompt: A circular sector has radius 5 and central angle 45 degrees. What is its area divided by π (exact decimal or integer)?

Solution: A/π = (θ/360)r^2 = (45/360)·5^2 = 3.125.


Answer: 8.333333333

Prompt: A circular sector has radius 10 and central angle 30 degrees. What is its area divided by π (exact decimal or integer)?

Solution: A/π = (θ/360)r^2 = (30/360)·10^2 = 8.333333333333334.


Answer: 21.33333333

Prompt: A circular sector has radius 8 and central angle 120 degrees. What is its area divided by π (exact decimal or integer)?

Solution: A/π = (θ/360)r^2 = (120/360)·8^2 = 21.333333333333332.


Answer: 24

Prompt: A circular sector has radius 12 and central angle 60 degrees. What is its area divided by π (exact decimal or integer)?

Solution: A/π = (θ/360)r^2 = (60/360)·12^2 = 24.0.


Answer: 33.33333333

Prompt: A circular sector has radius 10 and central angle 120 degrees. What is its area divided by π (exact decimal or integer)?

Solution: A/π = (θ/360)r^2 = (120/360)·10^2 = 33.333333333333336.


Answer: 8.333333333

Prompt: A circular sector has radius 5 and central angle 120 degrees. What is its area divided by π (exact decimal or integer)?

Solution: A/π = (θ/360)r^2 = (120/360)·5^2 = 8.333333333333334.


Answer: 1.333333333

Prompt: A circular sector has radius 4 and central angle 30 degrees. What is its area divided by π (exact decimal or integer)?

Solution: A/π = (θ/360)r^2 = (30/360)·4^2 = 1.3333333333333333.


Answer: 12.25

Prompt: A circular sector has radius 7 and central angle 90 degrees. What is its area divided by π (exact decimal or integer)?

Solution: A/π = (θ/360)r^2 = (90/360)·7^2 = 12.25.


Answer: 20.25

Prompt: A circular sector has radius 9 and central angle 90 degrees. What is its area divided by π (exact decimal or integer)?

Solution: A/π = (θ/360)r^2 = (90/360)·9^2 = 20.25.


Answer: 12

Prompt: A circular sector has radius 12 and central angle 30 degrees. What is its area divided by π (exact decimal or integer)?

Solution: A/π = (θ/360)r^2 = (30/360)·12^2 = 12.0.


Answer: 4.166666667

Prompt: A circular sector has radius 5 and central angle 60 degrees. What is its area divided by π (exact decimal or integer)?

Solution: A/π = (θ/360)r^2 = (60/360)·5^2 = 4.166666666666667.


Answer: 4

Prompt: A circular sector has radius 4 and central angle 90 degrees. What is its area divided by π (exact decimal or integer)?

Solution: A/π = (θ/360)r^2 = (90/360)·4^2 = 4.0.


Answer: 50

Prompt: A circular sector has radius 10 and central angle 180 degrees. What is its area divided by π (exact decimal or integer)?

Solution: A/π = (θ/360)r^2 = (180/360)·10^2 = 50.0.


Answer: 140

Prompt: What is lcm(10, 7, 4)?


Answer: 660

Prompt: What is lcm(10, 12, 11)?


Answer: 8

Prompt: What is lcm(4, 4, 8)?


Answer: 30

Prompt: What is lcm(10, 2, 3)?


Answer: 60

Prompt: What is lcm(10, 4, 6)?


Answer: 28

Prompt: What is lcm(4, 4, 7)?


Answer: 70

Prompt: What is lcm(5, 7, 10)?


Answer: 6

Prompt: What is lcm(6, 3, 6)?


Answer: 60

Prompt: What is lcm(5, 12, 10)?


Answer: 12

Prompt: What is lcm(6, 4, 12)?


Answer: 330

Prompt: What is lcm(6, 11, 10)?


Answer: 60

Prompt: What is lcm(3, 10, 12)?


Answer: 44

Prompt: What is lcm(4, 11, 11)?


Answer: 12

Prompt: What is lcm(4, 4, 12)?


Answer: 0

Prompt: Compute 7^7 mod 7.


Answer: 1

Prompt: Compute 2^3 mod 7.


Answer: 4

Prompt: Compute 6^8 mod 11.


Answer: 1

Prompt: Compute 8^7 mod 7.


Answer: 3

Prompt: Compute 9^8 mod 13.


Answer: 5

Prompt: Compute 6^6 mod 11.


Answer: 9

Prompt: Compute 8^5 mod 17.


Answer: 2

Prompt: Compute 3^8 mod 7.


Answer: 16

Prompt: Compute 4^6 mod 17.


Answer: 9

Prompt: Compute 9^6 mod 11.


Answer: 6

Prompt: Compute 7^7 mod 11.


Answer: 3

Prompt: Compute 7^8 mod 13.


Answer: 4

Prompt: Compute 7^6 mod 11.


Answer: 4

Prompt: Compute 7^4 mod 17.


Answer: 5

Prompt: Compute 3^5 mod 17.


Answer: 1

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [4, 3, 2, 1], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=2.5; MAD=1.0.


Answer: 1.375

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [5, 7, 10, 7], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=7.25; MAD=1.375.


Answer: 2.25

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [4, 3, 6, 10], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=5.75; MAD=2.25.


Answer: 2.875

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [12, 6, 4, 3], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=6.25; MAD=2.875.


Answer: 0.375

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [8, 9, 8, 8], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=8.25; MAD=0.375.


Answer: 2.5

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [5, 8, 1, 2], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=4.0; MAD=2.5.


Answer: 1.5

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [7, 9, 8, 4], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=7.0; MAD=1.5.


Answer: 2.75

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [4, 10, 6, 1], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=5.25; MAD=2.75.


Answer: 3

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [1, 5, 8, 10], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=6.0; MAD=3.0.


Answer: 2.25

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [11, 11, 8, 5], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=8.75; MAD=2.25.


Answer: 3.25

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [9, 1, 2, 7], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=4.75; MAD=3.25.


Answer: 2.75

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [3, 5, 12, 6], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=6.5; MAD=2.75.


Answer: 2.125

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [7, 6, 1, 7], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=5.25; MAD=2.125.


Answer: 3.5

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [1, 10, 9, 4], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=6.0; MAD=3.5.


Answer: 7

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (0,3) and (-1,-4) as a simplified rational (or integer)?


Answer: 0

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (1,3) and (2,3) as a simplified rational (or integer)?


Answer: 0

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (-1,4) and (5,4) as a simplified rational (or integer)?


Answer: 4

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (-4,-3) and (-3,1) as a simplified rational (or integer)?


Answer: 0

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (0,0) and (3,0) as a simplified rational (or integer)?


Answer: 5/7

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (-3,-2) and (4,3) as a simplified rational (or integer)?


Answer: 4/3

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (1,3) and (-5,-5) as a simplified rational (or integer)?


Answer: 3/11

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (-5,-3) and (6,0) as a simplified rational (or integer)?


Answer: -6

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (2,3) and (3,-3) as a simplified rational (or integer)?


Answer: 3/7

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (4,3) and (-3,0) as a simplified rational (or integer)?


Answer: -1/7

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (4,0) and (-3,1) as a simplified rational (or integer)?


Answer: 2/5

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (4,6) and (-1,4) as a simplified rational (or integer)?


Answer: 0

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (0,3) and (3,3) as a simplified rational (or integer)?


Answer: -7/2

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (2,6) and (4,-1) as a simplified rational (or integer)?


Answer: -5/2

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (2,-5) and (0,0) as a simplified rational (or integer)?


Answer: -2

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (5,-4) and (1,4) as a simplified rational (or integer)?


Answer: -3/2

Prompt: Complete the square (or use -b/2a) to find the x-coordinate of the vertex of y=2x^2 + (6)x + (5).


Answer: -2

Prompt: Complete the square (or use -b/2a) to find the x-coordinate of the vertex of y=1x^2 + (4)x + (2).


Answer: -3/2

Prompt: Complete the square (or use -b/2a) to find the x-coordinate of the vertex of y=2x^2 + (6)x + (4).


Answer: -3

Prompt: Complete the square (or use -b/2a) to find the x-coordinate of the vertex of y=1x^2 + (6)x + (-5).


Answer: 1

Prompt: Complete the square (or use -b/2a) to find the x-coordinate of the vertex of y=2x^2 + (-4)x + (3).


Answer: 1

Prompt: Complete the square (or use -b/2a) to find the x-coordinate of the vertex of y=2x^2 + (-4)x + (5).


Answer: 3

Prompt: Complete the square (or use -b/2a) to find the x-coordinate of the vertex of y=1x^2 + (-6)x + (4).


Answer: 2

Prompt: Complete the square (or use -b/2a) to find the x-coordinate of the vertex of y=1x^2 + (-4)x + (-5).


Answer: 1/2

Prompt: Complete the square (or use -b/2a) to find the x-coordinate of the vertex of y=2x^2 + (-2)x + (1).


Answer: -1

Prompt: Complete the square (or use -b/2a) to find the x-coordinate of the vertex of y=1x^2 + (2)x + (-2).


Answer: -1

Prompt: Complete the square (or use -b/2a) to find the x-coordinate of the vertex of y=2x^2 + (4)x + (4).


Answer: 90

Prompt: In the expansion of (1 + 3x)^5, what is the coefficient of x^2?


Answer: 5103

Prompt: In the expansion of (1 + 3x)^7, what is the coefficient of x^5?


Answer: 135

Prompt: In the expansion of (1 + 3x)^6, what is the coefficient of x^2?


Answer: 1512

Prompt: In the expansion of (1 + 3x)^8, what is the coefficient of x^3?


Answer: 1458

Prompt: In the expansion of (1 + 3x)^6, what is the coefficient of x^5?


Answer: 448

Prompt: In the expansion of (1 + 2x)^8, what is the coefficient of x^3?


Answer: 160

Prompt: In the expansion of (1 + 2x)^6, what is the coefficient of x^3?


Answer: 945

Prompt: In the expansion of (1 + 3x)^7, what is the coefficient of x^3?


Answer: 18

Prompt: In the expansion of (1 + 3x)^6, what is the coefficient of x^1?


Answer: 280

Prompt: In the expansion of (1 + 2x)^7, what is the coefficient of x^3?


Answer: 54

Prompt: In the expansion of (1 + 3x)^4, what is the coefficient of x^2?


Answer: 7

Prompt: Simplify log_5(a^5 · a^2) to an integer.


Answer: 8

Prompt: Simplify log_3(a^4 · a^4) to an integer.


Answer: 5

Prompt: Simplify log_5(a^3 · a^2) to an integer.


Answer: 5

Prompt: Simplify log_3(a^3 · a^2) to an integer.


Answer: 8

Prompt: Simplify log_2(a^5 · a^3) to an integer.


Answer: 6

Prompt: Simplify log_10(a^2 · a^4) to an integer.


Answer: 6

Prompt: Simplify log_3(a^2 · a^4) to an integer.


Answer: 9

Prompt: Simplify log_3(a^5 · a^4) to an integer.


Answer: 9

Prompt: Simplify log_10(a^5 · a^4) to an integer.


Answer: 7

Prompt: Simplify log_3(a^4 · a^3) to an integer.


Answer: 4

Prompt: Simplify log_5(a^2 · a^2) to an integer.


Answer: 4

Prompt: Simplify log_3(a^2 · a^2) to an integer.


Answer: 5

Prompt: Simplify log_10(a^3 · a^2) to an integer.


Answer: 1

Prompt: On the unit circle, what is the x-coordinate of the point at 0 degrees from the positive x-axis (standard position)?


Answer: 0

Prompt: On the unit circle, what is the x-coordinate of the point at 90 degrees from the positive x-axis (standard position)?


Answer: -1

Prompt: On the unit circle, what is the x-coordinate of the point at 180 degrees from the positive x-axis (standard position)?


Answer: 0

Prompt: On the unit circle, what is the x-coordinate of the point at 270 degrees from the positive x-axis (standard position)?


Answer: 1

Prompt: On the unit circle, what is the x-coordinate of the point at 360 degrees from the positive x-axis (standard position)?


Answer: If many keys collide, a bucket becomes a list (or similar) and lookup is O(n) in that bucket. Mitigations include randomized per-process hash seeds, switching collided buckets to balanced trees, and keeping load factor bounded with resizing.

Stay at the level of data-structure behaviour, not a specific CVE writeup.

Average-case lookup is O(1) under uniform hashing and a load-factor bound.

Adversarial or highly skewed keys can map to few buckets.

State the average-case assumption
Describe collision chains or trees
Name a mitigation

Prompt: Explain to a new engineer why a hash table can degrade to linear scan, and name one practical mitigation used in production languages.

human-authored teaching item; not executed

Solution: If many keys collide, a bucket becomes a list (or similar) and lookup is O(n) in that bucket. Mitigations include randomized per-process hash seeds, switching collided buckets to balanced trees, and keeping load factor bounded with resizing.


Answer: Atomicity: a transaction commits all of its writes or none. Consistency: committed transactions leave integrity rules intact. Isolation: concurrent transactions behave as if serialized per the advertised level. Durability: a committed transaction survives process crash (within the engine's durability contract).

Do not assume a particular database product.

The student already knows what a transaction is.

Define atomicity
Define consistency
Define isolation
Define durability

Prompt: Teach the four ACID properties with one sentence each, aimed at backend engineers.

Solution: Atomicity: a transaction commits all of its writes or none. Consistency: committed transactions leave integrity rules intact. Isolation: concurrent transactions behave as if serialized per the advertised level. Durability: a committed transaction survives process crash (within the engine's durability contract).


Answer: P: decision problems solvable in polynomial time on a deterministic TM. NP: decision problems whose yes-instances have polynomial-time verifiable certificates. P ⊆ NP is known; whether NP ⊆ P is open. NP-complete problems are the hardest in NP under poly-time reductions.

Avoid pop-science metaphors as the primary explanation.

P and NP are classes of decision problems on a deterministic vs nondeterministic Turing machine model (or equivalent).

Define P
Define NP
State the open question

Prompt: Give a precise, non-mystical explanation of P vs NP suitable for a CS undergrad who knows Big-O.

Solution: P: decision problems solvable in polynomial time on a deterministic TM. NP: decision problems whose yes-instances have polynomial-time verifiable certificates. P ⊆ NP is known; whether NP ⊆ P is open. NP-complete problems are the hardest in NP under poly-time reductions.


Answer: In 10,000 people, about 50 have the condition (0.5%). The test catches ~49.5 of them. Among 9,950 without the condition, 1% false positives ≈ 99.5 people. So about two-thirds of positives are false. A positive is evidence, not near-certainty.

A numeric posterior is welcome but not required if the base-rate point is clear.

Sensitivity = P(positive | disease)
Specificity = P(negative | no disease)

Compare false positives to true positives

Prompt: A test has 99% sensitivity and 99% specificity. Prevalence is 0.5%. Explain qualitatively whether a positive result means the person 'almost certainly' has the condition.

Solution: In 10,000 people, about 50 have the condition (0.5%). The test catches ~49.5 of them. Among 9,950 without the condition, 1% false positives ≈ 99.5 people. So about two-thirds of positives are false. A positive is evidence, not near-certainty.


Answer: Do not rebase commits that have been pushed to a shared branch unless the whole team agrees and force-push rules are explicit. Merge commits preserve the real integration topology, which helps incident reconstruction. Rebase is appropriate for local or explicitly throwaway feature branches before first share.

Do not rewrite commits that others have already based work on without an explicit agreement.

The repository is used by multiple people.

History will be used for blame and incident review.

Identify the danger of rewriting published history

Prompt: When should a team prefer merge commits over rebasing a shared branch? Give a short policy.

Solution: Do not rebase commits that have been pushed to a shared branch unless the whole team agrees and force-push rules are explicit. Merge commits preserve the real integration topology, which helps incident reconstruction. Rebase is appropriate for local or explicitly throwaway feature branches before first share.


Answer: Write-through: every write updates cache and backing store before completion; simpler consistency, higher write latency. Write-back: writes hit the cache and mark dirty; backing store updates later. Failure mode: a crash before flush loses dirty data unless another durability mechanism exists.

Single CPU, one cache, backing store is slower.

Define write-through
Define write-back
Name a failure mode

Prompt: Explain write-through vs write-back caching and one failure mode of write-back.

Solution: Write-through: every write updates cache and backing store before completion; simpler consistency, higher write latency. Write-back: writes hit the cache and mark dirty; backing store updates later. Failure mode: a crash before flush loses dirty data unless another durability mechanism exists.


Answer: Randomly assign A/B (and ideally a no-fertilizer control) to plots; replicate treatments; block on known gradients (sun, slope); fix harvest protocol and timing; pre-register the yield metric; keep application rates comparable.

The question is causal, not merely descriptive.

Randomization
Replication
Controls
Measurement protocol

Prompt: A lab wants to test whether fertilizer A beats fertilizer B on yield. List four design elements that make the comparison interpretable.

Solution: Randomly assign A/B (and ideally a no-fertilizer control) to plots; replicate treatments; block on known gradients (sun, slope); fix harvest protocol and timing; pre-register the yield metric; keep application rates comparable.


Answer: Unit-test pure decision logic and adapters with fakes when the branch space is large and I/O would drown signal. Integration-test the seams that actually fail in production: SQL, migrations, auth middleware, serialization. If a bug can only appear when two real components interact, it does not belong solely in a mocked unit test.

Avoid dogma that one layer is always enough.

The service has business logic, a database, and an HTTP API.

Locate the decision boundary
State cost vs confidence

Prompt: Give a practical rule for when a behaviour belongs in a unit test vs an integration test in a web service.

Solution: Unit-test pure decision logic and adapters with fakes when the branch space is large and I/O would drown signal. Integration-test the seams that actually fail in production: SQL, migrations, auth middleware, serialization. If a bug can only appear when two real components interact, it does not belong solely in a mocked unit test.


Answer: wait

Do not ship a change that hard-breaks a supported client

CPU +8% inside budget
p99 latency improved for large files
One client rejects new headers

Separate performance from compatibility
Treat compatibility as a gate

Prompt:
Three lab notes follow. Synthesize whether the team should ship the compression change.

Note A: CPU usage rose 8% in staging, well inside budget.
Note B: p99 latency on the image API fell 22% for files > 1 MB.
Note C: One internal client still uses a decoder that rejects the new frame header.
Answer ship, wait, or rollback and list the blocking issue if not ship.

human-authored synthesis from provided notes only

Solution: Latency and CPU look acceptable, but a known decoder incompatibility is a release blocker. Wait until that client is upgraded or gated.


Answer: bad_feature_flag_on_auth_gw_deploy

Prefer causes that explain locality and timing

az-b only
deploy 4 minutes prior
DB CPU flat
flag default true

Check what changed
Check where it changed
Rule out unchanged subsystems

Prompt:
Given these fragments, name the most likely primary cause (one phrase).
1) Errors spiked only in az-b.
2) Deploy of service auth-gw occurred in az-b 4 minutes earlier.
3) Database CPU was flat.
4) A feature flag defaulted to true in the new build.

Solution: The spatial and temporal coincidence with the az-b auth-gw deploy, plus a default-true flag, dominates; the database is not implicated.


Answer: prefer_stronger_consistency_for_shared_docs

Stay within the stated scenario
Do not invent statistics

Identify the objective
Name the main tradeoff
Give a bounded recommendation

Prompt: A team can add a strongly consistent cross-region write path or keep region-local writes with async replication. The product is a collaborative document editor. Which option better matches the product, and why, in 4 sentences or fewer?

Solution: Collaborative editors make concurrent conflicting writes user-visible as lost keystrokes or surprising ordering. Region-local async replication optimizes availability and latency at the cost of conflict. For this product, correctness of a shared document usually dominates extra cross-region latency. If a region outage is a bigger threat than edit conflicts, the opposite choice can be justified explicitly.


Answer: minimize_direct_identifiers_and_report_slice_metrics

Stay within the stated scenario
Do not invent statistics

Identify the objective
Name the main tradeoff
Give a bounded recommendation

Prompt: An evaluation set for hiring-assist models includes names and schools. State two concrete dataset practices that reduce avoidable harm without claiming fairness is solved.

Solution: Avoid keeping names, contact data, and other identifiers that are not needed to measure the skill. Report disaggregated error rates on documented slices (e.g., school groups) so failures are visible. Neither practice makes the system fair; they make the evaluation less casually harmful and more inspectable.


Answer: write spec, implement, code review

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 8 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 8: write spec, implement, code review (cost 8).


Answer: write spec, implement, code review, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 9 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 9: write spec, implement, code review, docs (cost 9).


Answer: write spec, implement, code review, qa

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 10 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 10: write spec, implement, code review, qa (cost 10).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 11 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 11: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 12 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 12: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 13 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 13: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 14 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 14: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 15 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 15: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 16 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 16: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 17 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 17: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 18 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 18: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 19 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 19: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 20 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 20: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 21 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 21: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 22 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 22: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 23 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 23: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 24 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 24: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 25 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 25: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 26 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 26: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 27 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 27: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 28 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 28: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 29 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 29: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 30 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 30: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 31 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 31: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 32 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 32: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 33 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 33: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 34 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 34: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 35 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 35: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 36 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 36: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 37 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 37: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 38 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 38: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 39 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 39: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 40 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 40: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 41 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 41: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 42 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 42: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 43 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 43: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 44 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 44: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 45 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 45: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 46 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 46: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 47 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 47: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 48 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 48: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 49 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 49: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 50 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 50: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 51 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 51: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 52 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 52: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 53 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 53: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 54 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 54: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 55 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 55: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 56 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 56: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 57 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 57: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 58 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 58: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 59 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 59: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 60 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 60: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 61 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 61: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 62 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 62: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 63 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 63: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 64 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 64: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 65 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 65: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 66 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 66: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 67 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 67: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 68 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 68: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 69 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 69: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 70 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 70: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 71 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 71: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 72 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 72: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 73 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 73: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 74 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 74: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 75 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 75: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 76 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 76: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 77 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 77: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 78 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 78: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 79 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 79: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 80 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 80: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 81 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 81: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 82 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 82: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 83 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 83: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 84 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 84: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 85 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 85: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 86 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 86: write spec, implement, code review, qa, docs (cost 11).


Answer: write spec, implement, code review, qa, docs

Priority order is fixed
No partial tasks

Walk the list
Take a task if it fits
Stop at first that does not

Prompt: You have 87 engineer-days this week. Tasks and costs: write spec=2, implement=5, code review=1, qa=2, docs=1. Select a prefix of the list (in the given priority order) that fits. Return the chosen task names comma-separated.

Solution: Greedy by listed priority until the next task would exceed 87: write spec, implement, code review, qa, docs (cost 11).


Answer: pairs=2; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 5 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(5/2) = 2; unpaired = 5 mod 2 = 1.


Answer: pairs=3; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 6 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(6/2) = 3; unpaired = 6 mod 2 = 0.


Answer: pairs=3; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 7 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(7/2) = 3; unpaired = 7 mod 2 = 1.


Answer: pairs=4; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 8 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(8/2) = 4; unpaired = 8 mod 2 = 0.


Answer: pairs=4; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 9 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(9/2) = 4; unpaired = 9 mod 2 = 1.


Answer: pairs=5; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 10 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(10/2) = 5; unpaired = 10 mod 2 = 0.


Answer: pairs=5; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 11 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(11/2) = 5; unpaired = 11 mod 2 = 1.


Answer: pairs=6; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 12 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(12/2) = 6; unpaired = 12 mod 2 = 0.


Answer: pairs=6; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 13 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(13/2) = 6; unpaired = 13 mod 2 = 1.


Answer: pairs=7; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 14 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(14/2) = 7; unpaired = 14 mod 2 = 0.


Answer: pairs=7; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 15 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(15/2) = 7; unpaired = 15 mod 2 = 1.


Answer: pairs=8; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 16 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(16/2) = 8; unpaired = 16 mod 2 = 0.


Answer: pairs=8; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 17 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(17/2) = 8; unpaired = 17 mod 2 = 1.


Answer: pairs=9; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 18 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(18/2) = 9; unpaired = 18 mod 2 = 0.


Answer: pairs=9; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 19 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(19/2) = 9; unpaired = 19 mod 2 = 1.


Answer: pairs=10; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 20 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(20/2) = 10; unpaired = 20 mod 2 = 0.


Answer: pairs=10; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 21 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(21/2) = 10; unpaired = 21 mod 2 = 1.


Answer: pairs=11; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 22 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(22/2) = 11; unpaired = 22 mod 2 = 0.


Answer: pairs=11; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 23 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(23/2) = 11; unpaired = 23 mod 2 = 1.


Answer: pairs=12; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 24 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(24/2) = 12; unpaired = 24 mod 2 = 0.


Answer: pairs=12; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 25 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(25/2) = 12; unpaired = 25 mod 2 = 1.


Answer: pairs=13; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 26 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(26/2) = 13; unpaired = 26 mod 2 = 0.


Answer: pairs=13; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 27 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(27/2) = 13; unpaired = 27 mod 2 = 1.


Answer: pairs=14; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 28 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(28/2) = 14; unpaired = 28 mod 2 = 0.


Answer: pairs=14; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 29 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(29/2) = 14; unpaired = 29 mod 2 = 1.


Answer: pairs=15; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 30 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(30/2) = 15; unpaired = 30 mod 2 = 0.


Answer: pairs=15; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 31 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(31/2) = 15; unpaired = 31 mod 2 = 1.


Answer: pairs=16; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 32 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(32/2) = 16; unpaired = 32 mod 2 = 0.


Answer: pairs=16; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 33 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(33/2) = 16; unpaired = 33 mod 2 = 1.


Answer: pairs=17; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 34 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(34/2) = 17; unpaired = 34 mod 2 = 0.


Answer: pairs=17; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 35 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(35/2) = 17; unpaired = 35 mod 2 = 1.


Answer: pairs=18; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 36 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(36/2) = 18; unpaired = 36 mod 2 = 0.


Answer: pairs=18; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 37 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(37/2) = 18; unpaired = 37 mod 2 = 1.


Answer: pairs=19; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 38 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(38/2) = 19; unpaired = 38 mod 2 = 0.


Answer: pairs=19; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 39 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(39/2) = 19; unpaired = 39 mod 2 = 1.


Answer: pairs=20; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 40 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(40/2) = 20; unpaired = 40 mod 2 = 0.


Answer: pairs=20; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 41 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(41/2) = 20; unpaired = 41 mod 2 = 1.


Answer: pairs=21; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 42 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(42/2) = 21; unpaired = 42 mod 2 = 0.


Answer: pairs=21; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 43 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(43/2) = 21; unpaired = 43 mod 2 = 1.


Answer: pairs=22; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 44 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(44/2) = 22; unpaired = 44 mod 2 = 0.


Answer: pairs=22; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 45 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(45/2) = 22; unpaired = 45 mod 2 = 1.


Answer: pairs=23; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 46 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(46/2) = 23; unpaired = 46 mod 2 = 0.


Answer: pairs=23; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 47 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(47/2) = 23; unpaired = 47 mod 2 = 1.


Answer: pairs=24; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 48 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(48/2) = 24; unpaired = 48 mod 2 = 0.


Answer: pairs=24; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 49 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(49/2) = 24; unpaired = 49 mod 2 = 1.


Answer: pairs=25; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 50 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(50/2) = 25; unpaired = 50 mod 2 = 0.


Answer: pairs=25; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 51 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(51/2) = 25; unpaired = 51 mod 2 = 1.


Answer: pairs=26; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 52 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(52/2) = 26; unpaired = 52 mod 2 = 0.


Answer: pairs=26; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 53 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(53/2) = 26; unpaired = 53 mod 2 = 1.


Answer: pairs=27; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 54 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(54/2) = 27; unpaired = 54 mod 2 = 0.


Answer: pairs=27; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 55 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(55/2) = 27; unpaired = 55 mod 2 = 1.


Answer: pairs=28; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 56 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(56/2) = 28; unpaired = 56 mod 2 = 0.


Answer: pairs=28; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 57 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(57/2) = 28; unpaired = 57 mod 2 = 1.


Answer: pairs=29; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 58 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(58/2) = 29; unpaired = 58 mod 2 = 0.


Answer: pairs=29; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 59 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(59/2) = 29; unpaired = 59 mod 2 = 1.


Answer: pairs=30; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 60 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(60/2) = 30; unpaired = 60 mod 2 = 0.


Answer: pairs=30; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 61 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(61/2) = 30; unpaired = 61 mod 2 = 1.


Answer: pairs=31; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 62 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(62/2) = 31; unpaired = 62 mod 2 = 0.


Answer: pairs=31; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 63 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(63/2) = 31; unpaired = 63 mod 2 = 1.


Answer: pairs=32; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 64 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(64/2) = 32; unpaired = 64 mod 2 = 0.


Answer: pairs=32; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 65 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(65/2) = 32; unpaired = 65 mod 2 = 1.


Answer: pairs=33; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 66 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(66/2) = 33; unpaired = 66 mod 2 = 0.


Answer: pairs=33; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 67 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(67/2) = 33; unpaired = 67 mod 2 = 1.


Answer: pairs=34; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 68 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(68/2) = 34; unpaired = 68 mod 2 = 0.


Answer: pairs=34; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 69 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(69/2) = 34; unpaired = 69 mod 2 = 1.


Answer: pairs=35; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 70 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(70/2) = 35; unpaired = 70 mod 2 = 0.


Answer: pairs=35; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 71 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(71/2) = 35; unpaired = 71 mod 2 = 1.


Answer: pairs=36; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 72 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(72/2) = 36; unpaired = 72 mod 2 = 0.


Answer: pairs=36; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 73 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(73/2) = 36; unpaired = 73 mod 2 = 1.


Answer: pairs=37; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 74 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(74/2) = 37; unpaired = 74 mod 2 = 0.


Answer: pairs=37; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 75 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(75/2) = 37; unpaired = 75 mod 2 = 1.


Answer: pairs=38; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 76 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(76/2) = 38; unpaired = 76 mod 2 = 0.


Answer: pairs=38; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 77 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(77/2) = 38; unpaired = 77 mod 2 = 1.


Answer: pairs=39; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 78 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(78/2) = 39; unpaired = 78 mod 2 = 0.


Answer: pairs=39; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 79 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(79/2) = 39; unpaired = 79 mod 2 = 1.


Answer: pairs=40; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 80 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(80/2) = 40; unpaired = 80 mod 2 = 0.


Answer: pairs=40; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 81 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(81/2) = 40; unpaired = 81 mod 2 = 1.


Answer: pairs=41; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 82 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(82/2) = 41; unpaired = 82 mod 2 = 0.


Answer: pairs=41; unpaired=1

People are indistinguishable for this count

Prompt: You must pair 83 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(83/2) = 41; unpaired = 83 mod 2 = 1.


Answer: pairs=42; unpaired=0

People are indistinguishable for this count

Prompt: You must pair 84 on-call engineers into two-person shifts. How many complete pairs can you form, and how many people are left unpaired?

Solution: pairs = floor(84/2) = 42; unpaired = 84 mod 2 = 0.


Answer: When a consumer cannot keep up, backpressure is a signal that slows or blocks the producer so queues stay bounded. A concrete implementation is a bounded blocking queue: put() waits when full. Alternatives include windowed credit in network protocols and dropping with a documented policy (which is load-shedding, not backpressure).

Be technically specific
No hidden chain-of-thought dump

State the mechanism
Give a concrete implication

Prompt: Explain backpressure in a producer-consumer pipeline and one concrete way to implement it.

Solution: When a consumer cannot keep up, backpressure is a signal that slows or blocks the producer so queues stay bounded. A concrete implementation is a bounded blocking queue: put() waits when full. Alternatives include windowed credit in network protocols and dropping with a documented policy (which is load-shedding, not backpressure).


Answer: Retries after uncertain network failure can otherwise capture twice. An idempotency key lets the server recognize a replay and return the original result instead of performing a second side effect. The client must reuse the same key for the same logical attempt and not reuse it for a different capture.

Be technically specific
No hidden chain-of-thought dump

State the mechanism
Give a concrete implication

Prompt: Why do payment capture APIs use idempotency keys? Answer for a programmer implementing retries.

Solution: Retries after uncertain network failure can otherwise capture twice. An idempotency key lets the server recognize a replay and return the original result instead of performing a second side effect. The client must reuse the same key for the same logical attempt and not reuse it for a different capture.


Answer: Statistical significance is not the same as practical significance or causal cleanliness. Ask: is 0.02pp worth the complexity and risk; were users randomized; is the metric gamed; are segments harmed; and does the experiment capture long-term effects.

Be technically specific
No hidden chain-of-thought dump

State the mechanism
Give a concrete implication

Prompt: A change improves conversion 0.02 percentage points with p<0.01 on 50 million sessions. What should a product meeting still ask?

Solution: Statistical significance is not the same as practical significance or causal cleanliness. Ask: is 0.02pp worth the complexity and risk; were users randomized; is the metric gamed; are segments harmed; and does the experiment capture long-term effects.


Answer: Pin seeds; pin software versions (lockfile or container digest); publish the exact split or generator with data hashes. Together these let someone regenerate the figure or show that they cannot.

Be technically specific
No hidden chain-of-thought dump

State the mechanism
Give a concrete implication

Prompt: A computational paper reports a figure but not the random seed, dependency versions, or input split. What three artifacts would make the figure independently checkable?

Solution: Pin seeds; pin software versions (lockfile or container digest); publish the exact split or generator with data hashes. Together these let someone regenerate the figure or show that they cannot.


Answer: An error budget is the allowed unreliability derived from an SLO (for example 0.1% unavailability in 30 days). It turns reliability from a slogan into a spending account: if budget remains, ship faster; if it is burned, freeze risky changes and invest in reliability until the SLO recovers.

Be technically specific
No hidden chain-of-thought dump

State the mechanism
Give a concrete implication

Prompt: In one paragraph, what is an error budget for and what decision does it unlock?

Solution: An error budget is the allowed unreliability derived from an SLO (for example 0.1% unavailability in 30 days). It turns reliability from a slogan into a spending account: if budget remains, ship faster; if it is burned, freeze risky changes and invest in reliability until the SLO recovers.


Answer: Float32 rounding is not associative; partial sums round differently depending on order and magnitude. Accumulate in float64 (or Kahan/Neumaier compensation) and cast once at the end if a 32-bit store is required.

Be technically specific
No hidden chain-of-thought dump

State the mechanism
Give a concrete implication

Prompt: Why can summing millions of float32 values depend on order? What is a safer accumulator type for a total?

Solution: Float32 rounding is not associative; partial sums round differently depending on order and magnitude. Accumulate in float64 (or Kahan/Neumaier compensation) and cast once at the end if a 32-bit store is required.