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The Socks in the Dark Riddle: How Many to Guarantee 3 Alike?
A drawer contains socks in five different colors. What is the minimum number of socks you must draw to guarantee having 3 socks of the same color?
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What is the answer to the socks in the dark riddle?
The answer is 11. In the worst case you could draw 2 socks of each of the 5 colors (10 socks) without a triple, so the 11th sock guarantees 3 of one color.
Why isn't the answer just 6 socks?
6 only guarantees 2 of the same color among 5 colors. To force 3 matching, you must beat the worst case of 2 per color (10 socks), so you need 11.
What math principle does this riddle use?
It uses the pigeonhole principle: with 5 colors, once you exceed 2 socks per color you are forced to have at least 3 of a single color.