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The Socks drawer
Robert’s Sock Drawer boasts 18 Black Socks, 10 Yellow, 8 Orange, 34 White and 2 Violet, not sorted by color.
The Light bulb has burned out. Robert cannot see what color the Socks are.
How many Socks does Robert have to take to be sure he has at least two Socks of the same color ?
Robert needs to take at least 6 socks
If Robert takes 5 socks, there could be one sock of each color, and he wouldn’t have at least two socks of the same color. However, if he takes a sixth sock, it must match one of the colors of the first 5 socks he picked. Therefore, he is guaranteed to have at least two socks of the same color.
Thus, Robert needs to take at least 6 socks to be sure he has at least two socks of the same color.