Math Puzzles

Read these first

1. 01Chinese Remainder Puzzles

   A puzzle gives you a number's remainder against several small divisors and asks you to find it, or to prove it's unique. The Chinese Remainder Theorem is the reusable machinery for turning a stack of remainder clues into one answer.

2. 02Counting by Bijection

   When a direct count gets messy, find a one-to-one correspondence to something you already know how to count. If every object in the hard pile matches exactly one object in the easy pile, the two piles are the same size.

3. 03Inclusion-Exclusion

   When events overlap, you can't just add their sizes, you'll double-count the overlap. Inclusion-exclusion is the systematic fix: add the singles, subtract the pairs, add back the triples, and so on.

Then the rest

1. 04Comparing Huge Powers Without a Calculator
2. 05Telescoping Sums and Products
3. 06The Substitution That Collapses the Algebra
4. 07AM-GM as a Puzzle Tool
5. 08Counting Lattice Paths
6. 09Fermat's Little Theorem in Puzzles
7. 10Finding the Last Digit of a Huge Power
8. 11GCD and LCM Puzzles
9. 12The Frobenius Coin Problem
10. 13Thinking in a Different Base
11. 14Vieta's Formulas: Answering Without Solving
12. 15Why Averaging Averages Gives the Wrong Answer
13. 16Catalan Numbers and Balanced Structures
14. 17Functional Equations
15. 18Nested Radicals and Infinite Fractions