The pigeonhole principle explained with a drawer of socks: a worked logical reasoning question

Worked solution

Correct answer: 3

The principle

Pigeonhole principle: with only two colour categories, a third item must repeat one of them.

Steps

1. There are only two possible colours: black and white.
2. Pulling out 2 socks could give one of each colour, so no pair is guaranteed yet.
3. Pulling out a 3rd sock must match one of the two colours already drawn, since no third colour exists.
4. So 3 socks are needed to guarantee a matching pair.

Heuristic to carry forward

With k categories, you need k+1 items pulled to guarantee at least two in the same category (pigeonhole principle).

Why each other answer is wrong

4

Overshoots the minimum; 3 already guarantees a match, so 4 is not the smallest sufficient number.

5

Further overshoots the minimum needed.

2

Two socks could be one of each colour, so a match is not yet guaranteed.