Please help me solve this problem:
Assuming that in a box there are $10$ black socks and $12$ blue socks, calculate the maximum number of socks needed to be drawn from the box before a pair of the same color can be made. Using the pigeonhole principle .
The pigeonhole principle: if $k$ is a positive integer and $k+1$ or more object are placed into $k$ boxes , than there is at least one box containing two or more of the object .
Three boxes.
Your "holes" are the two colors, and your "pigeons" are the socks. If you have three socks, two of them must be same color, forming a pair.