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Socks in the Dark (illustration)
FILE No.91Unsolved

Socks in the Dark

Difficulty ★☆☆about 3 minLogic PuzzleWorst casePigeonhole principle
A drawer of red, blue and black socks, no light. How many socks guarantee a matching pair?

Case Record

During a blackout, a detective wants a pair of socks. His drawer holds red, blue and black socks, many of each, all mixed up (no left or right).

He cannot see colours. A matching pair is two socks of the same colour.

Your question

How many socks must he pull out to be sure of having a matching pair, whatever he draws?

Case Files

Evidence

Diagram

The worst caseSocksWorst casePair?2Red, blue (different)No guarantee3Red, blue, blackNo guarantee4One colour must repeatGuaranteed
Diagram

Timeline

  1. Drawing socks in the dark.

Hints

If you get stuck, open the hints one at a time, in order.

Open hint 1

With 3 socks, could all be different colours?

Open hint 2

What happens with the 4th sock?

Open hint 3

Think of the worst case.

Solve It

Your question

How many socks must he pull out to be sure of having a matching pair, whatever he draws?

Choose the answer closest to the truth.

Share: I'm solving this

The Truth

4

The answer is: 4.

With 3 socks they might be red, blue and black, with no pair. The fourth sock must match one of the three colours. Think of the worst case: number of colours + 1.

Colours + 1Worst case: the first 3 are all different coloursThe 4th must match one of themAnswer: 3 + 1 = 4
Diagram of the solution

Key Points

  • Think of the worst case
  • Number of colours + 1 guarantees a pair
  • The next sock after all different

Why people get fooled

People imagine lucky draws, so they think 2 socks will do.

Similar tricks

  • The worst-case type
  • The pigeonhole type

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