Multiple choice general knowledge math & puzzles

It is dark in my bedroom and I want to get two socks of the same color from my drawer, which contains 24 red and 24 blue socks. How many socks do I have to take from the drawer to get at least two socks of the same color?

  1. 2

  2. 3

  3. 24

  4. 47
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

By the pigeonhole principle, with 2 colors of socks, you need to pick 3 socks to guarantee a matching pair. The worst case is picking 1 red and 1 blue first - the third sock must match one of them. Picking just 2 socks might give different colors, and 24 or 47 are far more than necessary.

AI explanation

To answer this question, we can use the concept of the Pigeonhole Principle.

The Pigeonhole Principle states that if you have more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon.

In this case, each color of socks represents a pigeonhole, and the number of socks of each color represents the number of pigeons.

Since we have 24 red socks and 24 blue socks, we have a total of 48 socks in 2 different colors, which means we have 48 "pigeons".

To guarantee that we have at least two socks of the same color, we need to take one more sock than the number of colors. In this case, we have 2 colors (red and blue), so we need to take at least 3 socks.

Therefore, the correct answer is B) 3.

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