Question

A drawer contains 10 black and 10 brown socks which are all mixed up. What is the fewest number of socks you can take from the drawer without looking and be sure to get a pair of the same color?

• A. 7 pairs
• B. 7 pieces only
• C. 10 pieces only
• D. 3 pieces only

Answer 1

The Correct Option is D

To solve this problem, we need to determine the fewest number of socks to draw without looking in order to guarantee getting a pair of the same color. A drawer contains 10 black and 10 brown socks, adding up to 20 socks in total. Initially, we consider the worst-case scenario where we draw as many socks as possible without obtaining a pair of the same color.

1. If we draw 1 sock, it can be either black or brown.
2. If we draw a 2nd sock, it may still not form a pair as it could be of the other color.
3. Drawing a 3rd sock ensures that at least two socks will be of the same color, inevitably forming a pair.

Thus, the fewest number of socks needed to guarantee obtaining at least one matched pair is 3 pieces only, making this the correct option.