You’re faced with a cozy yet classic problem in logic:

Your drawer holds:

  • 2 red socks
  • 20 yellow socks
  • 31 blue socks

You pick socks at random, without looking.

Question: What’s the minimum number of socks you must pull out to guarantee a matching pair in the same color?

Step 1: Understand the Worst-Case Scenario

This is a classic case for the pigeonhole principle, which states:

If you have more items than containers, at least one container must hold more than one item.

In this context:

  • There are 3 colors (red, yellow, blue) — think of these as “pigeonholes”.
  • You want to be guaranteed that at least one color repeats — i.e., a pair.

Worst Case

You could pick:

  • 1 red sock
  • 1 yellow sock
  • 1 blue sock

That’s 3 socks, all different colors—no match yet.

Step 2: One More Guarantees a Match

Once you pull a 4th sock, it must match one of the previous three (since there are only 3 colors available).

Therefore:

Minimum number of socks = 4

This guarantees at least one matching pair in the same color.

Final Answer

You must pull out at least 4 socks to guarantee a matching pair of the same color.

Reference