# What is the smallest number of gloves you need to select to guarantee at least one matching pair?

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There are 40 gloves in a drawer: 10 pair of white gloves, 5 pairs of black gloves, 3 pairs of brown, and 2 pairs of gray. You select the gloves in the dark and can check them only after a selection has been made. What is the smallest number of gloves you need to select to guarantee at least one matching pair?

posted Aug 8, 2017

+1 vote

You need to select at least 5 Gloves to be fully sure of having a matching pair.

Upto 4 selection there is a chance that all four are of different color. One additional will make sure that you have a matching pair.

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What is the fewest number of pairs you need to test to guarantee you can get the flashlight on?

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A man challenges the greatest chess player in the world to two games of chess. He guarantees that he will win or tie at least one of the games for sure. To be even more cocky, the man says he will play both games at the same time.

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There is an air base on the equator. The maximum amount of fuel that a plane can contain would be only sufficient for it to fly halfway around the world.

For at least one plane to finish a trip around the world, how many planes do you need at least?

A trip around the world!
Logic Level 3

There is an air base on the equator. The maximum amount of fuel that a plane can contain would be only sufficient for it to fly halfway around the world.

For at least one plane to finish a trip around the world, how many planes do you need at least?

Details and assumptions:
Same plane doesn't depart twice or more.
The airplanes can use their fuel until it's empty. Starting the airplane doesn't take any time.
Every plane moves at the same speed, and on the same airway.
Assume the planes and air base are dimensionless, and thus, can turn directions instantly.
The plane can only be fueled via aerial refueling, and the amount of time the process takes is negligible.
Every plane starts at the air base and must return to the air base.