problem stringlengths 21 332 | thinking_trace stringlengths 44 456 | answer stringlengths 1 147 |
|---|---|---|
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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Check out the documentation for more information.
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:
- Problem decomposition — break the problem into manageable steps
- Formula recall — state the relevant equation or approach
- Step-by-step computation — perform each operation with intermediate values
- Self-verification — check the result via alternative method or substitution
- 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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