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!

### Puzzles you will enjoy

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The Mismatched Socks : r/puzzles

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