Sequence & Pattern Puzzles

Read these first

1. 01How to Crack a What-Comes-Next Question

   'What's the next number in 2, 6, 12, 20, 30, ...?' is really asking whether you have a checklist for sequence puzzles. Differences, ratios, and known sequence families cover almost everything you'll be handed.

2. 02Turning a Word Puzzle Into a Recurrence

   Most 'count the ways to...' interview puzzles are recurrences wearing a costume. The skill is translating a story into an equation that relates the answer for n to the answer for smaller n, after that, it's mechanical.

3. 03Generating Functions as a Puzzle Tool

   A generating function packs an entire infinite sequence into one polynomial-like expression, where the coefficient of x^n is the n-th answer. Counting problems that look hard as combinatorics often become easy algebra once repackaged this way.

Then the rest

1. 04Detecting Cycles in an Iterated Sequence
2. 05Does This Recursion Converge
3. 06Fixed Points of Iterated Maps
4. 07Solving Linear Recurrences With Characteristic Roots
5. 08Summing an Infinite Series in Your Head
6. 09Where Fibonacci Numbers Show Up