Overview
This is the friendliest face of the pigeonhole principle: with more items than categories, some category must repeat.
How to solve Socks in the Dark
- There are only two colours (categories).
- Two socks might be one of each colour — no guaranteed pair yet.
- A third sock must repeat one of the two colours, guaranteeing a pair.
The key insight
To guarantee a pair you need one more item than there are colours: colours + 1. The count of socks in the drawer is irrelevant.
Variations & echoes
- With 3 colours you'd need 4 socks; with k colours, k+1.
- Pigeonhole proves surprising facts, like two people in a city with the same number of hairs.
Frequently asked questions
Does the number of socks matter?
No — as long as both colours are present, three pulls always suffice.