Shoes in a Closet

Probability Level 2

There are 16 pairs of shoes in a closet. 9 pairs are blue, 4 pairs are green and 3 pairs are purple. If someone takes one shoe out at a time, what is the least number of shoes they have to pull out in order to be sure that they have a pair of every colour?


The answer is 30.

Addie Mendelson by Addie Mendelson , 16, Hong Kong

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2 solutions

Isabelle Hsu
Jan 30, 2019

In the worst case scenario, you would pull out 9 pairs of blue shoes, which is 18 shoes. And then you would pull out 4 pairs of greens shoes which is 8 shoes. Then you could pull out 3 purple left shoes and the next one is guaranteed to be a purple, right shoe. So, by then, you would've pulled out 30 shoes. Great Job👍

2 Helpful 0 Interesting 1 Brilliant 0 Confused
Addie Mendelson
Jan 31, 2019

You have to think of the worst case scenario. In a worst case scenario, you would pull out 9 pairs, 18 shoes of blue shoes. And 4 pairs, 8 shoes of green shoes. Then you might pull out 3 purple [left] shoes. So you would have to pull one more out which has to be a purple [right] shoe. So, in total you had pulled out 30 shoes

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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