Problem Solving

pritam.ryders wrote:24 each grey and white colour hand gloves are mixed up in a drawer.
What's the minimum number of gloves you need to take out (blindly) to be sure of having a matching pair

To begin, if you take out 2 socks, there's a chance that you will have 1 white sock and 1 gray sock.
However, once you take out the 3rd sock, it will be either white or gray, so you can be certain that you will have a matching pair.

Answer: 3

Note: This is neither a counting question nor a probability question. It uses something called the Pigeonhole Principle.

Cheers,
Brent

Hi pritam.ryders,

There's a detail worth noting in this question. Since the question is NOT a probability/permutation/combination question, the starting number of grey gloves and white gloves is IRRELEVANT (as long as there are at least 2 of each color). There are only 2 colors, so you would have to grab 3 gloves to GUARANTEE a matching pair.

With that same idea in mind, if there were 3 different colors, how many gloves would you need to pull to GUARANTEE a matching pair?

GMAT assassins aren't born, they're made,
Rich

Hi mikepamlyla,

That is absolutely CORRECT. Nicely reasoned.

GMAT assassins aren't born, they're made,
Rich

Hi vipulgoyal,

This is more of a logic question than a math question:

Think of it like this: the goal is to have a matching pair of socks.

1st sock: either gray or white (it doesn't matter)
2nd sock: If it's the same color as the first, then you have a matching pair, but there's no guarantee that it will match (it might be the other color)

Now, if you have 1 gray and 1 white, then then the 3rd sock is GUARANTEED to match one or the other.

This is the MINIMUM number of socks that must be pulled to guarantee a matching pair.

GMAT assassins aren't born, they're made,
Rich