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Matching Socks Puzzle: Pick Minimum Number of Socks

Matching Socks Puzzle: Pick Minimum Number of Socks

Imagine you need a pair of matching blue socks in your dark room. Your drawer holds 63 socks: 31 black, 15 blue, and 17 red, all identical to touch. Can you pick the minimum number of socks guaranteed to include at least one blue pair, without seeing the colors?

Time to discover the number: 3 minutes.

Let's use logic to solve this difficult situation of matching socks blindly!

Solution to the matching socks puzzle of taking out at least one pair of blue socks

Picking Minimum number of Socks

We'll tackle this with a "what-if" approach. What happens if we grab a bunch of socks, but have an unlucky streak, pulling out only black and red?

The Worst Case Scenario

Let's say we take out a fistful of 48 socks – the sum of the two highest sock counts (black and red). Yikes! In this (highly unlikely) scenario, we might still end up with zero blue socks.

But wait, there's more!

What if we grab just one more sock, making it 49 total? In this new scenario (with 48 black and red socks with one more sock), the 49th guarantees a blue (at least one blue sock)!

Even that doesn't make a pair, it's just one blue sock!

The Answer

To be 100% certain of picking at least a blue pair, we need to grab a minimum of 50 socks.

So, next time you're rummaging in the dark, remember – grabbing 50 (two more than the sum of the two highest sock counts) ensures at least one blue pair, even in the tricky situation of picking the socks in a dark room!


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