25 quant brainteasers and logic questions with answers

How to approach these questions

A brainteaser becomes manageable when you identify what cannot change or how much information each action reveals. These examples build from simple impossibility arguments to strategic games, logical implications and estimates. Say the reasoning aloud: an interviewer should be able to follow why the answer is forced, rather than being asked to trust a remembered trick.

Sample questions, answers and explanations

Try each question before reading its answer. These original teaching examples remain free to read on this page.

328 brainteaser/logic questions from the bank

Each question has its own page with a short answer and a credit to its source. Hints and full worked solutions are in the question bank with a free account.

1. Five pirates splitting a hundred gold coinsMedium
2. Monotone lattice paths across a six-by-six boardEasy
3. Re-flipping only the heads until a uniform resultMedium
4. Opening move in a race to fiftyMedium
5. Repunit-style numbers whose product equals their sumMedium
6. Time to fire three shots from a six-shooterEasy
7. Ten tasters finding one poisoned wine barrelMedium
8. Bacteria count after forty more minutesEasy
9. Group size forcing a shared birth monthEasy
10. Is 1027 primeEasy
11. Wine fraction after mixing two diluted glassesEasy
12. Triangles from prime-difference chords on a circleHard
13. Ages that are sums of powers in a 19th-century lifeMedium
14. Photo line with heights falling away from the middleMedium
15. One six in four rolls versus double six in 24Medium
16. Finding one heavy bean among eightEasy
17. Three uniforms falling in a set orderEasy
18. Regular polygons with whole-degree interior anglesEasy
19. Length of a river from drifting and swimming timesEasy
20. Dollars and cents swap after spending halfMedium
21. Integers up to ten thousand containing a zeroEasy
22. Weighing a fish from its head, body and tailEasy
23. Perfect shuffles needed to restore a deckHard
24. Total of all digits from one to a millionMedium
25. Size of a partial deck from three remaindersEasy
26. Share of dogs in an endless line of petsMedium
27. Power-of-two ball game where taking the last losesHard
28. Two mowers sharing one lawnEasy
29. Who sits left of person five at a round tableEasy
30. Grabbing socks blindly until two matchEasy
31. Shipping oil a thousand miles with leaky relaysMedium
32. Adults at a concert before a bus arrivesMedium
33. Price alternately falling and rising one percentEasy
34. Four walkers and one lantern on a narrow bridgeEasy
35. Finishing position from distances to last and halfwayEasy
36. Number whose first six multiples permute its digitsMedium
37. Next time the clock hands coincide after noonEasy
38. Ants released from both ends of a stringEasy
39. Pascal row with neighbouring entries in ratio 3 to 4 to 5Medium
40. Which of four switches lights the bulbEasy
41. Picking the safest full house before a random dealMedium
42. Two hoses against an open drainEasy
43. Most sides a cube's shadow can haveMedium
44. Days for ten growing lily pads to cover a pondMedium
45. Next calendar date with eight different digitsMedium
46. How many plums balance one pearMedium
47. Five-digit numbers starting 37 with rotations divisible by 37Hard
48. Most likely final die face when passing 1000Easy
49. One percent daily growth for one hundred daysEasy
50. Identical bikes and a total spoke countMedium

What our question-bank data shows

Subtopic coverage in the bank

Bank difficulty labels: 192 easy · 112 medium · 51 hard.

Lessons behind the techniques

Use these lesson previews to find the definitions and derivations behind the worked examples.

• Sample Spaces, Events, and the Probability Axioms
• Counting and Combinatorics
• Conditional Probability, Total Probability, and Bayes' Rule
• Series and the Geometric Series: Partial Sums and Convergence
• Optimisation Problems
• Expectation, Mean, and Variance

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