Brainteasers & Puzzles

Read these first

1. 01How to Attack a Brainteaser

   A repeatable five-move routine for puzzles you have never seen before, pin the rules, shrink the problem, hunt for the quantity that does not change, guess the shape of the answer, then try to break it.

2. 02Balance-Scale Weighing Problems

   Twelve coins, one fake of unknown weight, three weighings. The puzzle looks like luck but it is pure information budgeting, every weighing has three outcomes, so aim to split the live possibilities into three equal thirds.

3. 03Hat-Colour Problems

   A room of people can see everyone's hat but their own. With no communication except silence and timing, they can still pass information, and that trick is the seed of every hat puzzle an interviewer will throw at you.

4. 04Invariants and Monovariants

   Two of the most reusable tools in puzzle solving. An invariant is a quantity no legal move can change, which proves things impossible; a monovariant only moves one way, which proves things must end.

Then the rest

1. 05Parity Arguments
2. 06Ants on a Pole and Collision Arguments
3. 07Colouring and Tiling Arguments
4. 08Counting Information to Bound the Answer
5. 09Counting the Same Thing Two Ways
6. 10Geometric Probability Puzzles
7. 11Induction and Recursive Structure in Puzzles
8. 12Light-Bulb Switching Problems
9. 13Making a Fair Coin From a Biased One
10. 14Nim and Winning Positions
11. 15River-Crossing and Bridge-Torch Problems
12. 16Symmetry Arguments
13. 17The Birthday Problem
14. 18The Coupon-Collector Problem
15. 19The Extremal Principle
16. 20The Hundred Prisoners and the Boxes
17. 21The Monty Hall Problem
18. 22The Prisoners and the Light Switch