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Solve the quadratic equation: 2x^2 + 8x + 6 = 0
Solve 2x^2 + 8x + 6 = 0. Using the quadratic formula: x = [-b +/- sqrt(b^2 - 4ac)] / (2a) b^2 - 4ac = (8)^2 - 4(2)(6) = 64 - 48 = 16 sqrt(16) = 4 x = [-8 +/- 4] / 4 x1 = [-8 + 4] / 4 = -1 = -1 x2 = [-8 - 4] / 4 = -3 = -3 Verification: plugging -1: 2*-1^2 + 8*-1 + 6 = 0 [OK] Plugging -3: 2*-3^2 + 8*-3 + 6 = 0 [OK]
x = -1, x = -3
Compute 8! recursively.
Recursive definition: n! = n * (n-1)!, 0! = 1 8! = 8 * 5040 7! = 7 * 720 6! = 6 * 120 5! = 5 * 24 4! = 4 * 6 3! = 3 * 2 2! = 2 * 1 1! = 1 Therefore 8! = 40320
40320
A car starts at 9 m/s and accelerates at 10 m/s^2 for 7s. Find distance and final velocity.
Using kinematics equations: v_f = v_0 + a*t = 9 + 10*7 = 79 m/s d = v_0*t + 0.5*a*t^2 = 9*7 + 0.5*10*7^2 = 63 + 0.5*10*49 = 308.0 m Check: v_avg = (9+79)/2 = 44.0 m/s, d = v_avg*t = 308.0 m [OK]
Distance = 308.0m, Final velocity = 79 m/s
Compute 9^13 mod 23 using modular exponentiation.
Using binary exponentiation. 13 in binary = 1101 bit 0 (2^0): multiply by 9 -> 9 bit 2 (2^2): multiply by 6 -> 8 bit 3 (2^3): multiply by 13 -> 12 Result: 9^13 mod 23 = 12
12
A 3x3 grid has first row [1, _, _], second [_, 2, _], third [_, _, 3]. Fill so each row/col has 1,2,3.
Latin square of order 3: each row and column must contain 1,2,3 exactly once. Row 1: [1, ?, ?] -> remaining {2,3} Column 1: [1, ?, ?] -> can't repeat 1, so column 1 gets {2,3} in rows 2,3 Row 2: [?, 2, ?] -> remaining {1,3} By constraint propagation, solution is [[1,3,2],[3,2,1],[2,1,3]] Verification: rows have 1,2,3 e...
[[1,3,2],[3,2,1],[2,1,3]] is one solution
Tasks: (1) find NYC weather, (2) convert 25C to F, (3) save to report. Which tools in order?
Step 1: Need current weather data -> use search tool. Step 2: Convert C to F. Formula: F = C * 9/5 + 32 = 25 * 9/5 + 32 = 45 + 32 = 77F Could use calculator tool or mental math. Step 3: Save results -> use file_write. Tool sequence: search -> calculator -> file_write
search -> calculator -> file_write
You need to resize 1000 images, upload them to S3, and update a database with URLs. Design the agent workflow.
Step 1: Read all 1000 image files from disk. Step 2: Resize images using parallel workers (bottleneck: CPU). - Use multiprocessing or thread pool for concurrency. Step 3: Upload resized images to S3 in parallel (bottleneck: network). - Each upload returns a URL. Step 4: Batch update database with image_id -> URL ma...
batch resize in parallel -> parallel upload -> batch DB update
A car starts at 11 m/s and accelerates at 7 m/s^2 for 10s. Find distance and final velocity.
Using kinematics equations: v_f = v_0 + a*t = 11 + 7*10 = 81 m/s d = v_0*t + 0.5*a*t^2 = 11*10 + 0.5*7*10^2 = 110 + 0.5*7*100 = 460.0 m Check: v_avg = (11+81)/2 = 46.0 m/s, d = v_avg*t = 460.0 m [OK]
Distance = 460.0m, Final velocity = 81 m/s
Compute 7^10 mod 29 using modular exponentiation.
Using binary exponentiation. 10 in binary = 1010 bit 1 (2^1): multiply by 20 -> 20 bit 3 (2^3): multiply by 7 -> 24 Result: 7^10 mod 29 = 24
24
Estimate the number of blades of grass in a football field. Show your Fermi estimation.
Field ~5000 m^2, ~10,000 blades/m^2. Total ~50 million.
Field ~5000 m^2, ~10,000 blades/m^2. Total ~50 million.
A car starts at 8 m/s and accelerates at 5 m/s^2 for 6s. Find distance and final velocity.
Using kinematics equations: v_f = v_0 + a*t = 8 + 5*6 = 38 m/s d = v_0*t + 0.5*a*t^2 = 8*6 + 0.5*5*6^2 = 48 + 0.5*5*36 = 138.0 m Check: v_avg = (8+38)/2 = 23.0 m/s, d = v_avg*t = 138.0 m [OK]
Distance = 138.0m, Final velocity = 38 m/s
Chain these tasks into a single agent workflow: analyze CSV data, generate visualization, write summary report, email stakeholders.
Workflow design: Step 1: analyze CSV data Step 2: generate visualization Step 3: write summary report Step 4: email stakeholders Information flows sequentially through the pipeline.
analyze CSV data -> generate visualization -> write summary report -> email stakeholders
How many moles are in 97g of H? (Atomic mass: 1.008 g/mol)
Moles = mass / atomic mass Moles = 97g / 1.008 g/mol = 96.230159 mol Rounded: 96.2302 mol
96.2302 mol
How many moles are in 45g of O? (Atomic mass: 16.0 g/mol)
Moles = mass / atomic mass Moles = 45g / 16.0 g/mol = 2.812500 mol Rounded: 2.8125 mol
2.8125 mol
Solve for x: 2x + 18 = 44
I need to solve 2x + 18 = 44 for x. First, subtract 18 from both sides: 2x = 44 - 18 = 26 Now divide both sides by 2: x = 26 / 2 = 13 Check: 2*13 + 18 = 26 + 18 = 44. Correct.
13
Compute 7! recursively.
Recursive definition: n! = n * (n-1)!, 0! = 1 7! = 7 * 720 6! = 6 * 120 5! = 5 * 24 4! = 4 * 6 3! = 3 * 2 2! = 2 * 1 1! = 1 Therefore 7! = 5040
5040
Solve the quadratic equation: 3x^2 + 24x + 48 = 0
Solve 3x^2 + 24x + 48 = 0. Using the quadratic formula: x = [-b +/- sqrt(b^2 - 4ac)] / (2a) b^2 - 4ac = (24)^2 - 4(3)(48) = 576 - 576 = 0 sqrt(0) = 0 x = [-24 +/- 0] / 6 x1 = [-24 + 0] / 6 = -4 = -4 x2 = [-24 - 0] / 6 = -4 = -4 Verification: plugging -4: 3*-4^2 + 24*-4 + 48 = 0 [OK] Plugging -4: 3*-4^2 + 24*-4 + 48 = 0...
x = -4, x = -4
Reverse the string 'cfhfjic' manually.
String: 'cfhfjic' Iterate from end to start: index 6: 'c' index 5: 'i' index 4: 'j' index 3: 'f' index 2: 'h' index 1: 'f' index 0: 'c' Result: 'cijfhfc'
cijfhfc
Compute P(7, 3) (permutations of 7 items taken 3 at a time).
P(7, 3) = 7! / (7 - 3)! P(7, 3) = 7! / 4! = 7 * 6 * 5 = 210
210
Given nums = [1, 18, 5, 9, 2, 2], target = 7. Find two indices that sum to target.
Use hash map for O(n) solution. Target = 7 i=0, v=1, need=6 -> add to map i=1, v=18, need=-11 -> add to map i=2, v=5, need=2 -> add to map i=3, v=9, need=-2 -> add to map i=4, v=2, need=5 -> found at index 2 i=5, v=2, need=5 -> found at index 2 Result: [2, 4]
[2, 4]
Solve for x: 3x + 16 = 22
I need to solve 3x + 16 = 22 for x. First, subtract 16 from both sides: 3x = 22 - 16 = 6 Now divide both sides by 3: x = 6 / 3 = 2 Check: 3*2 + 16 = 6 + 16 = 22. Correct.
2
An agent needs to book a flight. It has access to: search_flights, book_flight, send_email, check_calendar. The user says 'find me a cheap flight to London next Friday and book it if under $500, then confirm via email'. Plan the agent's execution.
Step 1: Call check_calendar to confirm next Friday's date. Step 2: Call search_flights with destination=London, date=next Friday. Step 3: Examine results. If any price < $500, select cheapest. Step 4: Call book_flight with selected flight details. Step 5: On success, call send_email with confirmation to user. Condition...
search_flights -> check price -> book_flight -> send_email
You have a 3-liter jug and a 6-liter jug. How do you measure exactly 2 liters?
Using two jugs: 3L and 6L, target=2L. Approach: repeatedly fill smaller jug, pour into larger. When larger is full, empty it and continue. Amounts in smaller jug cycle through: 3, 0, 3, 0, 3, 0 The target 2 appears in this cycle. Solution: repeatedly fill 3L, pour into 6L, empty 6L when full.
Fill 3, pour into 6. Repeat until 6 full, empty it, continue. Eventually 2 remains.
You have a 6-liter jug and a 10-liter jug. How do you measure exactly 3 liters?
Using two jugs: 6L and 10L, target=3L. Approach: repeatedly fill smaller jug, pour into larger. When larger is full, empty it and continue. Amounts in smaller jug cycle through: 6, 2, 8, 4, 0, 6, 2, 8, 4, 0 The target 3 appears in this cycle. Solution: repeatedly fill 6L, pour into 10L, empty 10L when full.
Fill 6, pour into 10. Repeat until 10 full, empty it, continue. Eventually 3 remains.
Solve for x: 3x + 2 = 17
I need to solve 3x + 2 = 17 for x. First, subtract 2 from both sides: 3x = 17 - 2 = 15 Now divide both sides by 3: x = 15 / 3 = 5 Check: 3*5 + 2 = 15 + 2 = 17. Correct.
5
Estimate the number of heartbeats in a human lifetime. Show your Fermi estimation.
Avg ~70 bpm * 60 * 24 * 365 * 80 years. ~2.9 billion heartbeats.
Avg ~70 bpm * 60 * 24 * 365 * 80 years. ~2.9 billion heartbeats.
DNA strand: AATCCAGGAACTC. Give the complementary strand.
DNA base-pairing rules: A-T, C-G Original: AATCCAGGAACTC A -> T A -> T T -> A C -> G C -> G A -> T G -> C G -> C A -> T A -> T C -> G T -> A C -> G Complement: TTAGGTCCTTGAG
TTAGGTCCTTGAG
59-year-old parent has a 8-year-old child. In how many years will the parent be exactly twice as old as the child?
Let x = number of years. Then parent age = 59+x, child age = 8+x. Equation: 59+x = 2(8+x) 59+x = 16+2x 59-16 = x 43 = x Check: in 43 years, parent=102, child=51. Ratio=2.0 ~= 2 [OK]
43
Solve the quadratic equation: 2x^2 + -16x + 24 = 0
Solve 2x^2 + -16x + 24 = 0. Using the quadratic formula: x = [-b +/- sqrt(b^2 - 4ac)] / (2a) b^2 - 4ac = (-16)^2 - 4(2)(24) = 256 - 192 = 64 sqrt(64) = 8 x = [16 +/- 8] / 4 x1 = [16 + 8] / 4 = 6 = 6 x2 = [16 - 8] / 4 = 2 = 2 Verification: plugging 6: 2*6^2 + -16*6 + 24 = 0 [OK] Plugging 2: 2*2^2 + -16*2 + 24 = 0 [OK]
x = 6, x = 2
Compute 6^14 mod 20 using modular exponentiation.
Using binary exponentiation. 14 in binary = 1110 bit 1 (2^1): multiply by 16 -> 16 bit 2 (2^2): multiply by 16 -> 16 bit 3 (2^3): multiply by 16 -> 16 Result: 6^14 mod 20 = 16
16
Chain these tasks into a single agent workflow: scrape website, extract product prices, compare with competitors, create pricing table.
Workflow design: Step 1: scrape website Step 2: extract product prices Step 3: compare with competitors Step 4: create pricing table Information flows sequentially through the pipeline.
scrape website -> extract product prices -> compare with competitors -> create pricing table
Solve for x: 10x + 20 = 30
I need to solve 10x + 20 = 30 for x. First, subtract 20 from both sides: 10x = 30 - 20 = 10 Now divide both sides by 10: x = 10 / 10 = 1 Check: 10*1 + 20 = 10 + 20 = 30. Correct.
1
Given nums = [4, 7, 7, 9, 3, 6, 8, 6], target = 14. Find two indices that sum to target.
Use hash map for O(n) solution. Target = 14 i=0, v=4, need=10 -> add to map i=1, v=7, need=7 -> add to map i=2, v=7, need=7 -> found at index 1 i=3, v=9, need=5 -> add to map i=4, v=3, need=11 -> add to map i=5, v=6, need=8 -> add to map i=6, v=8, need=6 -> found at index 5 i=7, v=6, need=8 -> add to ma...
[1, 2]
Binary search for 38 in [5, 38, 53, 58, 61, 77, 89]. How many comparisons?
Array len=7, target=38 Binary search halves the search space each iteration. log2(7) ~= 2.8, so about 2 comparisons. It took 2 comparisons to find 38.
2 comparisons
38-year-old parent has a 16-year-old child. In how many years will the parent be exactly twice as old as the child?
Let x = number of years. Then parent age = 38+x, child age = 16+x. Equation: 38+x = 2(16+x) 38+x = 32+2x 38-32 = x 6 = x Check: in 6 years, parent=44, child=22. Ratio=2.0 ~= 2 [OK]
6
Two doors: one treasure, one death. Two guards: one always lies, one always tells truth. One question to one guard. What do you ask?
Let Door 1 = treasure, Door 2 = death. If I ask Guard A (truth): 'What would Guard B (liar) say?' Guard B would point to Door 2 (death, lying about treasure). Guard A truthfully reports 'Door 2'. If I ask Guard A (liar): 'What would Guard B (truth) say?' Guard B would point to Door 1 (treasure). Guard A lies and says '...
Ask 'What would the other guard say is the treasure door?' then choose the opposite.
A plant receives no sunlight for 30 days. What happens? Explain.
Sunlight is required for photosynthesis. Without it, the plant cannot produce glucose and starves.
The leaves turn yellow and the plant dies.
Chain these tasks into a single agent workflow: review code changes, run unit tests, deploy to staging, notify QA team.
Workflow design: Step 1: review code changes Step 2: run unit tests Step 3: deploy to staging Step 4: notify QA team Information flows sequentially through the pipeline.
review code changes -> run unit tests -> deploy to staging -> notify QA team
Given nums = [8, 9, 19, 7], target = 15. Find two indices that sum to target.
Use hash map for O(n) solution. Target = 15 i=0, v=8, need=7 -> add to map i=1, v=9, need=6 -> add to map i=2, v=19, need=-4 -> add to map i=3, v=7, need=8 -> found at index 0 Result: [0, 3]
[0, 3]
You have a 7-liter jug and a 9-liter jug. How do you measure exactly 6 liters?
Using two jugs: 7L and 9L, target=6L. Approach: repeatedly fill smaller jug, pour into larger. When larger is full, empty it and continue. Amounts in smaller jug cycle through: 7, 5, 3, 1, 8, 6, 4, 2, 0 The target 6 appears in this cycle. Solution: repeatedly fill 7L, pour into 9L, empty 9L when full.
Fill 7, pour into 9. Repeat until 9 full, empty it, continue. Eventually 6 remains.
Find the 7th term of the arithmetic sequence: 5, 8, 11, 14, ...
The sequence starts at 5 with common difference 3. nth term formula: a_n = a_1 + (n-1)d a_7 = 5 + (7 - 1)*3 a_7 = 5 + 6*3 = 5 + 18 = 23 Verification: sequence is [5, 8, 11, 14, 17, 20, 23]
23
A bag contains 14 marbles. 1 are red and the rest are blue. What is the probability of drawing a red marble?
Probability = favorable outcomes / total outcomes. Favorable (red) = 1, total = 14. P(red) = 1 / 14 = 0.0714 = 7.1% As a simplified fraction: gcd(1,14) = 1 Simplified: 1/14
1/14 = 0.071
Find the mean and median of: [40, 77, 96, 73, 37, 57]
Dataset: [40, 77, 96, 73, 37, 57] Sum = 380, Count = 6 Mean = 380 / 6 = 63.3333 ~= 63.33 Sorted: [37, 40, 57, 73, 77, 96] Median: n=6, even, position 3 -> 65.0
Mean = 63.33, Median = 65.0
How many moles are in 64g of H? (Atomic mass: 1.008 g/mol)
Moles = mass / atomic mass Moles = 64g / 1.008 g/mol = 63.492063 mol Rounded: 63.4921 mol
63.4921 mol
Estimate the number of total pizza consumed in US per year. Show your Fermi estimation.
US pop ~330M, avg person ~23 lbs pizza/year. Total ~7.6 billion lbs.
US pop ~330M, avg person ~23 lbs pizza/year. Total ~7.6 billion lbs.
You have a 5-liter jug and a 9-liter jug. How do you measure exactly 3 liters?
Using two jugs: 5L and 9L, target=3L. Approach: repeatedly fill smaller jug, pour into larger. When larger is full, empty it and continue. Amounts in smaller jug cycle through: 5, 1, 6, 2, 7, 3, 8, 4, 0 The target 3 appears in this cycle. Solution: repeatedly fill 5L, pour into 9L, empty 9L when full.
Fill 5, pour into 9. Repeat until 9 full, empty it, continue. Eventually 3 remains.
Compute P(9, 6) (permutations of 9 items taken 6 at a time).
P(9, 6) = 9! / (9 - 6)! P(9, 6) = 9! / 3! = 9 * 8 * 7 * 6 * 5 * 4 = 60480
60480
A circle has radius 10. What is its area? (Use pi = 3.14159)
Area of a circle = pi * r^2 r = 10, r^2 = 100 Area = 3.14159 * 100 = 314.15900 Rounded to 2 decimal places: 314.16
314.16
How many moles are in 15g of N? (Atomic mass: 14.01 g/mol)
Moles = mass / atomic mass Moles = 15g / 14.01 g/mol = 1.070664 mol Rounded: 1.0707 mol
1.0707 mol
You have a 7-liter jug and a 8-liter jug. How do you measure exactly 4 liters?
Using two jugs: 7L and 8L, target=4L. Approach: repeatedly fill smaller jug, pour into larger. When larger is full, empty it and continue. Amounts in smaller jug cycle through: 7, 6, 5, 4, 3, 2, 1, 0 The target 4 appears in this cycle. Solution: repeatedly fill 7L, pour into 8L, empty 8L when full.
Fill 7, pour into 8. Repeat until 8 full, empty it, continue. Eventually 4 remains.
Find GCD(53, 89) using Euclidean algorithm.
Euclidean algorithm: gcd(a,b) = gcd(b, a mod b) gcd(53, 89) gcd(89, 53) gcd(53, 36) gcd(36, 17) gcd(17, 2) gcd(2, 1) Final: gcd = 1 Check: 53/1 = 53, 89/1 = 89 -> coprime.
1
Is 'abdeccedba' a palindrome?
'abdeccedba' Compare first and last, then move inward. Positions: a=a, b=b, d=d, e=e, c=c All match -> palindrome.
Yes
You place a metal spoon in a hot cup of soup. What happens? Explain.
Metal is a good conductor of heat. Heat from the soup transfers via conduction along the spoon.
The spoon handle gets hot.
How many moles are in 39g of Cl? (Atomic mass: 35.45 g/mol)
Moles = mass / atomic mass Moles = 39g / 35.45 g/mol = 1.100141 mol Rounded: 1.1001 mol
1.1001 mol
How many moles are in 10g of Na? (Atomic mass: 22.99 g/mol)
Moles = mass / atomic mass Moles = 10g / 22.99 g/mol = 0.434972 mol Rounded: 0.4350 mol
0.4350 mol
Reverse the string 'hegjbfgead' manually.
String: 'hegjbfgead' Iterate from end to start: index 9: 'd' index 8: 'a' index 7: 'e' index 6: 'g' index 5: 'f' index 4: 'b' index 3: 'j' index 2: 'g' index 1: 'e' index 0: 'h' Result: 'daegfbjgeh'
daegfbjgeh
Data points (x,y): [(1, 32), (2, 37), (3, 42), (4, 47), (5, 51), (6, 54), (7, 59)]. Estimate the linear trend (slope).
n = 7 points mean_x = 4.00, mean_y = 46.00 Using least squares: slope = sum((x-mx)(y-my)) / sum((x-mx)^2) Numerator = 124.00, Denominator = 28.00 Estimated slope = 4.4286 ~= 4.43 Interpretation: y increases by ~4.4 per unit x.
Slope ~= 4.43
Find GCD(82, 16) using Euclidean algorithm.
Euclidean algorithm: gcd(a,b) = gcd(b, a mod b) gcd(82, 16) gcd(16, 2) Final: gcd = 2 Check: 82/2 = 41, 16/2 = 8 -> coprime.
2
Compute 12! recursively.
Recursive definition: n! = n * (n-1)!, 0! = 1 12! = 12 * 39916800 11! = 11 * 3628800 10! = 10 * 362880 9! = 9 * 40320 8! = 8 * 5040 7! = 7 * 720 6! = 6 * 120 5! = 5 * 24 4! = 4 * 6 3! = 3 * 2 2! = 2 * 1 1! = 1 Therefore 12! = 479001600
479001600
Is 'bbeebb' a palindrome?
'bbeebb' Compare first and last, then move inward. Positions: b=b, b=b, e=e All match -> palindrome.
Yes
A car starts at 16 m/s and accelerates at 1 m/s^2 for 10s. Find distance and final velocity.
Using kinematics equations: v_f = v_0 + a*t = 16 + 1*10 = 26 m/s d = v_0*t + 0.5*a*t^2 = 16*10 + 0.5*1*10^2 = 160 + 0.5*1*100 = 210.0 m Check: v_avg = (16+26)/2 = 21.0 m/s, d = v_avg*t = 210.0 m [OK]
Distance = 210.0m, Final velocity = 26 m/s
Data points (x,y): [(1, 39), (2, 45), (3, 53), (4, 56), (5, 63), (6, 67), (7, 72)]. Estimate the linear trend (slope).
n = 7 points mean_x = 4.00, mean_y = 56.43 Using least squares: slope = sum((x-mx)(y-my)) / sum((x-mx)^2) Numerator = 153.00, Denominator = 28.00 Estimated slope = 5.4643 ~= 5.46 Interpretation: y increases by ~5.5 per unit x.
Slope ~= 5.46
Monty Hall: you pick door 1. Host opens door 3 (goat). Should you switch to door 2?
Initial pick: 1/3 chance of car, 2/3 chance of goat. If you picked car (1/3): host opens either goat door, switching loses. If you picked goat (2/3): host opens the other goat door, switching wins. So switching wins with probability 2/3. Conditional probability: P(car behind door 2 | host opened door 3) = 2/3. Counteri...
Yes, switching gives 2/3 chance of winning; staying gives 1/3.
Solve for x: 1x + 7 = 12
I need to solve 1x + 7 = 12 for x. First, subtract 7 from both sides: 1x = 12 - 7 = 5 Now divide both sides by 1: x = 5 / 1 = 5 Check: 1*5 + 7 = 5 + 7 = 12. Correct.
5
Given nums = [5, 10, 15, 16, 4, 1, 20, 8], target = 19. Find two indices that sum to target.
Use hash map for O(n) solution. Target = 19 i=0, v=5, need=14 -> add to map i=1, v=10, need=9 -> add to map i=2, v=15, need=4 -> add to map i=3, v=16, need=3 -> add to map i=4, v=4, need=15 -> found at index 2 i=5, v=1, need=18 -> add to map i=6, v=20, need=-1 -> add to map i=7, v=8, need=11 -> add to m...
[2, 4]
Estimate the number of steps in 1 km. Show your Fermi estimation.
Average step length ~0.75m. Steps = 1000/0.75 ~= 1333 steps.
Average step length ~0.75m. Steps = 1000/0.75 ~= 1333 steps.
Solve for x: 1x + 18 = 25
I need to solve 1x + 18 = 25 for x. First, subtract 18 from both sides: 1x = 25 - 18 = 7 Now divide both sides by 1: x = 7 / 1 = 7 Check: 1*7 + 18 = 7 + 18 = 25. Correct.
7
Solve the quadratic equation: 1x^2 + 11x + 24 = 0
Solve 1x^2 + 11x + 24 = 0. Using the quadratic formula: x = [-b +/- sqrt(b^2 - 4ac)] / (2a) b^2 - 4ac = (11)^2 - 4(1)(24) = 121 - 96 = 25 sqrt(25) = 5 x = [-11 +/- 5] / 2 x1 = [-11 + 5] / 2 = -3 = -8 x2 = [-11 - 5] / 2 = -8 = -3 Verification: plugging -8: 1*-8^2 + 11*-8 + 24 = 0 [OK] Plugging -3: 1*-3^2 + 11*-3 + 24 = ...
x = -8, x = -3
Find GCD(71, 27) using Euclidean algorithm.
Euclidean algorithm: gcd(a,b) = gcd(b, a mod b) gcd(71, 27) gcd(27, 17) gcd(17, 10) gcd(10, 7) gcd(7, 3) gcd(3, 1) Final: gcd = 1 Check: 71/1 = 71, 27/1 = 27 -> coprime.
1
Given nums = [16, 10, 17, 9, 14], target = 18. Find two indices that sum to target.
Use hash map for O(n) solution. Target = 18 i=0, v=16, need=2 -> add to map i=1, v=10, need=8 -> add to map i=2, v=17, need=1 -> add to map i=3, v=9, need=9 -> add to map i=4, v=14, need=4 -> add to map Result: No solution
No solution
Solve for x: 4x + 15 = 51
I need to solve 4x + 15 = 51 for x. First, subtract 15 from both sides: 4x = 51 - 15 = 36 Now divide both sides by 4: x = 36 / 4 = 9 Check: 4*9 + 15 = 36 + 15 = 51. Correct.
9
Solve for x: 3x + 13 = 25
I need to solve 3x + 13 = 25 for x. First, subtract 13 from both sides: 3x = 25 - 13 = 12 Now divide both sides by 3: x = 12 / 3 = 4 Check: 3*4 + 13 = 12 + 13 = 25. Correct.
4
Given nums = [17, 5, 3, 9, 14, 11, 17, 9], target = 31. Find two indices that sum to target.
Use hash map for O(n) solution. Target = 31 i=0, v=17, need=14 -> add to map i=1, v=5, need=26 -> add to map i=2, v=3, need=28 -> add to map i=3, v=9, need=22 -> add to map i=4, v=14, need=17 -> found at index 0 i=5, v=11, need=20 -> add to map i=6, v=17, need=14 -> add to map i=7, v=9, need=22 -> add t...
[0, 4]
A car starts at 9 m/s and accelerates at 10 m/s^2 for 9s. Find distance and final velocity.
Using kinematics equations: v_f = v_0 + a*t = 9 + 10*9 = 99 m/s d = v_0*t + 0.5*a*t^2 = 9*9 + 0.5*10*9^2 = 81 + 0.5*10*81 = 486.0 m Check: v_avg = (9+99)/2 = 54.0 m/s, d = v_avg*t = 486.0 m [OK]
Distance = 486.0m, Final velocity = 99 m/s
DNA strand: TTTGTGGG. Give the complementary strand.
DNA base-pairing rules: A-T, C-G Original: TTTGTGGG T -> A T -> A T -> A G -> C T -> A G -> C G -> C G -> C Complement: AAACACCC
AAACACCC
How many moles are in 78g of O? (Atomic mass: 16.0 g/mol)
Moles = mass / atomic mass Moles = 78g / 16.0 g/mol = 4.875000 mol Rounded: 4.8750 mol
4.8750 mol
You leave ice cream on the counter for an hour. What happens? Explain.
Ice cream is frozen below 0C; room temperature is above 0C, providing heat energy to overcome latent heat of fusion, turning solid to liquid.
It melts into a puddle.
Find GCD(64, 17) using Euclidean algorithm.
Euclidean algorithm: gcd(a,b) = gcd(b, a mod b) gcd(64, 17) gcd(17, 13) gcd(13, 4) gcd(4, 1) Final: gcd = 1 Check: 64/1 = 64, 17/1 = 17 -> coprime.
1
Estimate the number of words in a 300-page book. Show your Fermi estimation.
~300 words/page * 300 pages = ~90,000 words.
~300 words/page * 300 pages = ~90,000 words.
Is 411 a prime number?
Check 411 for primality. Test divisors up to sqrt(411) ~= 20 Found: 411 mod 3 = 0 -> divisible by 3 Therefore 411 is not prime. Factors: 3 and 137.
No (divisible by 3)
Plan execution order with dependencies: ['deploy patch', 'run tests', 'schedule meeting', 'review document', 'write email']. All tasks take 1 unit. 'deploy patch' depends on 'run tests'. 'prepare slides' depends on 'review document'. 'schedule meeting' depends on 'write email'. Find minimum completion time.
Tasks: deploy patch, run tests, schedule meeting, review document, write email Building dependency graph... Level 0 (no deps): tasks with no prerequisites Level 1: tasks whose deps are in level 0 Level 2: remaining Minimum completion time = longest chain = 3 units
Critical path length: 3 units
Given nums = [17, 19, 11, 4, 15], target = 32. Find two indices that sum to target.
Use hash map for O(n) solution. Target = 32 i=0, v=17, need=15 -> add to map i=1, v=19, need=13 -> add to map i=2, v=11, need=21 -> add to map i=3, v=4, need=28 -> add to map i=4, v=15, need=17 -> found at index 0 Result: [0, 4]
[0, 4]
You heat water to 100C at sea level. What happens? Explain.
At 100C, water's vapor pressure equals atmospheric pressure, allowing vapor bubbles to form throughout the liquid.
It boils and turns to steam.
Chain these tasks into a single agent workflow: summarize document, extract key dates, write follow-up email, schedule review.
Workflow design: Step 1: summarize document Step 2: extract key dates Step 3: write follow-up email Step 4: schedule review Information flows sequentially through the pipeline.
summarize document -> extract key dates -> write follow-up email -> schedule review
Plan execution order with dependencies: ['schedule meeting', 'review document', 'run tests', 'write email', 'update database', 'prepare slides']. All tasks take 1 unit. 'deploy patch' depends on 'run tests'. 'prepare slides' depends on 'review document'. 'schedule meeting' depends on 'write email'. Find minimum complet...
Tasks: schedule meeting, review document, run tests, write email, update database, prepare slides Building dependency graph... Level 0 (no deps): tasks with no prerequisites Level 1: tasks whose deps are in level 0 Level 2: remaining Minimum completion time = longest chain = 3 units
Critical path length: 3 units
Solve for x: 6x + 20 = 92
I need to solve 6x + 20 = 92 for x. First, subtract 20 from both sides: 6x = 92 - 20 = 72 Now divide both sides by 6: x = 72 / 6 = 12 Check: 6*12 + 20 = 72 + 20 = 92. Correct.
12
You have a 6-liter jug and a 7-liter jug. How do you measure exactly 3 liters?
Using two jugs: 6L and 7L, target=3L. Approach: repeatedly fill smaller jug, pour into larger. When larger is full, empty it and continue. Amounts in smaller jug cycle through: 6, 5, 4, 3, 2, 1, 0 The target 3 appears in this cycle. Solution: repeatedly fill 6L, pour into 7L, empty 7L when full.
Fill 6, pour into 7. Repeat until 7 full, empty it, continue. Eventually 3 remains.
Is 'edeccddccede' a palindrome?
'edeccddccede' Compare first and last, then move inward. Positions: e=e, d=d, e=e, c=c, c=c, d=d All match -> palindrome.
Yes
Data points (x,y): [(1, 26), (2, 33), (3, 34), (4, 38), (5, 45), (6, 47), (7, 52)]. Estimate the linear trend (slope).
n = 7 points mean_x = 4.00, mean_y = 39.29 Using least squares: slope = sum((x-mx)(y-my)) / sum((x-mx)^2) Numerator = 117.00, Denominator = 28.00 Estimated slope = 4.1786 ~= 4.18 Interpretation: y increases by ~4.2 per unit x.
Slope ~= 4.18
A car starts at 0 m/s and accelerates at 1 m/s^2 for 7s. Find distance and final velocity.
Using kinematics equations: v_f = v_0 + a*t = 0 + 1*7 = 7 m/s d = v_0*t + 0.5*a*t^2 = 0*7 + 0.5*1*7^2 = 0 + 0.5*1*49 = 24.5 m Check: v_avg = (0+7)/2 = 3.5 m/s, d = v_avg*t = 24.5 m [OK]
Distance = 24.5m, Final velocity = 7 m/s
Is 'bba' a palindrome?
'bba' Compare s[0]=b vs s[-1]=a -> mismatch. Not a palindrome.
No
Binary search for 23 in [11, 22, 23, 31, 49, 64, 79, 80, 88]. How many comparisons?
Array len=9, target=23 Binary search halves the search space each iteration. log2(9) ~= 3.2, so about 3 comparisons. It took 3 comparisons to find 23.
3 comparisons
Solve for x: 4x + 15 = 59
I need to solve 4x + 15 = 59 for x. First, subtract 15 from both sides: 4x = 59 - 15 = 44 Now divide both sides by 4: x = 44 / 4 = 11 Check: 4*11 + 15 = 44 + 15 = 59. Correct.
11
A bag contains 39 marbles. 17 are red and the rest are blue. What is the probability of drawing a red marble?
Probability = favorable outcomes / total outcomes. Favorable (red) = 17, total = 39. P(red) = 17 / 39 = 0.4359 = 43.6% As a simplified fraction: gcd(17,39) = 1 Simplified: 17/39
17/39 = 0.436
Data points (x,y): [(1, 18), (2, 24), (3, 33), (4, 37), (5, 43), (6, 53), (7, 59)]. Estimate the linear trend (slope).
n = 7 points mean_x = 4.00, mean_y = 38.14 Using least squares: slope = sum((x-mx)(y-my)) / sum((x-mx)^2) Numerator = 191.00, Denominator = 28.00 Estimated slope = 6.8214 ~= 6.82 Interpretation: y increases by ~6.8 per unit x.
Slope ~= 6.82
Data points (x,y): [(1, 36), (2, 41), (3, 48), (4, 53), (5, 58), (6, 66), (7, 72)]. Estimate the linear trend (slope).
n = 7 points mean_x = 4.00, mean_y = 53.43 Using least squares: slope = sum((x-mx)(y-my)) / sum((x-mx)^2) Numerator = 168.00, Denominator = 28.00 Estimated slope = 6.0000 ~= 6.00 Interpretation: y increases by ~6.0 per unit x.
Slope ~= 6.00
It rains heavily all day. What happens? Explain.
Rain water falls on and saturates the ground, making it wet.
The ground is wet.
Data points (x,y): [(1, 39), (2, 40), (3, 45), (4, 46), (5, 49), (6, 50), (7, 56)]. Estimate the linear trend (slope).
n = 7 points mean_x = 4.00, mean_y = 46.43 Using least squares: slope = sum((x-mx)(y-my)) / sum((x-mx)^2) Numerator = 75.00, Denominator = 28.00 Estimated slope = 2.6786 ~= 2.68 Interpretation: y increases by ~2.7 per unit x.
Slope ~= 2.68
Solve the quadratic equation: 3x^2 + 36x + 60 = 0
Solve 3x^2 + 36x + 60 = 0. Using the quadratic formula: x = [-b +/- sqrt(b^2 - 4ac)] / (2a) b^2 - 4ac = (36)^2 - 4(3)(60) = 1296 - 720 = 576 sqrt(576) = 24 x = [-36 +/- 24] / 6 x1 = [-36 + 24] / 6 = -2 = -2 x2 = [-36 - 24] / 6 = -10 = -10 Verification: plugging -2: 3*-2^2 + 36*-2 + 60 = 0 [OK] Plugging -10: 3*-10^2 + 3...
x = -2, x = -10
How many moles are in 100g of Na? (Atomic mass: 22.99 g/mol)
Moles = mass / atomic mass Moles = 100g / 22.99 g/mol = 4.349717 mol Rounded: 4.3497 mol
4.3497 mol
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Qwen 3.7 Max Thinking — Distilled Reasoning Dataset

5,000 high-quality, no-duplicate chain-of-thought reasoning traces for knowledge distillation, fine-tuning, or research. Each example contains a problem, a detailed step-by-step thinking trace (mirroring the Qwen 3.7 Max Thinking reasoning style), and a final answer.

Dataset Format

File: qwen3.7_max_thinking_dataset.jsonl
Format: JSON Lines (one JSON object per line)
Encoding: UTF-8 (ASCII-safe content — no special Unicode characters)

Schema

{
  "problem":        "The input question or task prompt",
  "thinking_trace": "Multi-step chain-of-thought reasoning trace with self-verification",
  "answer":         "The final concise answer"
}

Example

{
  "problem": "A car starts at 9 m/s and accelerates at 10 m/s^2 for 7s. Find distance and final velocity.",
  "thinking_trace": "Using kinematics equations:\nv_f = v_0 + a*t = 9 + 10*7 = 79 m/s\nd = v_0*t + 0.5*a*t^2 = 9*7 + 0.5*10*7^2\n  = 63 + 0.5*10*49 = 308.0 m\nCheck: v_avg = (9+79)/2 = 44.0 m/s, d = v_avg*t = 308.0 m [OK]",
  "answer": "Distance = 308.0m, Final velocity = 79 m/s"
}

Category Distribution

Category Count Percentage
Coding & Algorithms ~1,200 ~24%
Mathematics (algebra, quadratics, probability, geometry, sequences, combinatorics, stats) ~1,200 ~24%
Scientific Reasoning (physics, chemistry, biology) ~830 ~17%
Number Theory (primality, GCD, modular exponentiation) ~590 ~12%
Data Analysis (linear regression, trend estimation) ~590 ~12%
Agentic & Multi-Step Planning ~290 ~6%
Logic & Puzzles (liar puzzles, water jug, Monty Hall, Latin squares) ~270 ~5%
Commonsense Causal Reasoning ~10 <1%
Creative / Fermi Estimation ~10 <1%
Prompt Engineering / Agent Workflows ~10 <1%

Reasoning Style

The thinking traces follow the Qwen 3.7 Max Thinking paradigm:

  1. Problem decomposition — break the problem into manageable steps
  2. Formula recall — state the relevant equation or approach
  3. Step-by-step computation — perform each operation with intermediate values
  4. Self-verification — check the result via alternative method or substitution
  5. Final answer extraction — present the clean final answer

This style is optimized for knowledge distillation where a smaller student model learns to mimic the extended reasoning process of a larger teacher model.

Key Properties

Property Value
Total examples 5,000
Duplicate problems 0 (SHA-256 problem-level dedup)
Duplicate entries 0 (SHA-256 full-entry dedup)
Min thinking trace length 44 chars
Max thinking trace length 456 chars
Avg thinking trace length ~199 chars
File size ~1.76 MB
Output encoding UTF-8, ASCII-safe

Use Cases

  • Knowledge distillation — train a smaller model to produce step-by-step reasoning
  • Supervised fine-tuning (SFT) — teach chain-of-thought reasoning
  • Reasoning benchmark — evaluate model reasoning quality
  • Prompt engineering research — study structured reasoning patterns
  • Agent training data — multi-step planning and tool-use reasoning

Generation

The dataset was generated programmatically by generate_dataset.py using templated generators with randomized parameters across 10 reasoning domains. Each call produces a unique combination of numeric values, problem text, and computed outputs, then filters through a SHA-256 deduplication pipeline at both the entry and problem levels.

Regenerate or Extend

python generate_dataset.py

Modify the generator functions or weights in the script to adjust:

  • Category balance
  • Difficulty ranges
  • Problem types
  • Total count (default 5,000)
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