A drawer has 31 black, 15 blue, and 17 red socks. Find the minimum socks you must draw with eyes closed to ensure getting at least one pair of blue socks.

### The Minimum Number of Socks Riddle

A man has in his drawer **31 black socks, 15 blue socks**, and **17 red socks**. The room is completely dark. He cannot see the color of the socks. What is the **minimum number of socks** he must take out to be **absolutely sure of getting at least one pair of blue socks?**

**Time to solve:** 5 minutes.

With logic, you would find this riddle relatively easy to solve.

### Solution to the Minimum Number of Socks Logic Puzzle: Taking Out Minimum number of Socks to Ensure at Least One Blue Pair

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?

This is the Worst Case Scenario Analysis. This problem solving technique used widely in solving management problems, but can also help in solving puzzles to real life problems.

#### The Worst Case Scenario Analysis

Let's say we take out a bunch of 48 socks—the sum of the two sock counts other than blue (sum of black and red). Ohh..., even in this large number socks picked up, we might end up with not a single blue sock. Why, you might wonder. This is simply because all the black and red socks ended up in the bunch you picked up with not a solitary blue sock. Highly unlikely, still a possibility—the worst possible situation.

Don't get disheartened. **Take one step forward!** **Pick up one more sock.** *From Worst Case Analysis to another What if analysis situation.*

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 sock** *(at least one blue sock)*! All red and black socks already are in your worst case bunch of 48 socks.

**Even that doesn't make a pair, it's just one blue sock!** Now no need to imagine another what-if situation. Solution is pretty clear.

#### The Answer

To be 100% certain of picking at least a blue pair, you need to take out from the drawer one more, a **minimum of 50** (worst case 48 plus 2) socks.

So, the next time if you face such a problem, remember—taking out 50 (two more than the sum of the two other color sock counts) ensures at least the one color pair you want, even in the tricky situation of picking the socks in a dark room!

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