Gloves Galore!

Probability Level 3

It is now winter, and Sam is now going back to school! This time, he needs gloves. he has 6 pairs of blue gloves and 6 pairs of white gloves and the gloves are all mixed up. He must grab a pair in complete darkness. He wants a 100 percent chance of getting a pair. He doesn't care whether it's a blue pair or a white pair, and the gloves can be different colours.

What is the least number of gloves he needs to grab?


The answer is 13.

Bj Prognome by bj prognome , 46, USA

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2 solutions

Sharky Kesa
Jul 22, 2014

This question isn't that well clarified.

6 pairs of blue and white gloves each means that there are 12 left gloves and 12 right gloves. If you pick 12 gloves, you might get all gloves of the left hand. If you pick 13 however you are guaranteed to have a pair of gloves of the same colour.

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Please tell me which parts are not well clarified so I can fix it.

bj prognome - 6 years, 10 months ago

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Can you write that he wants a pair of left and right gloves. Otherwise you could have 2 left gloves or 2 right gloves.

Sharky Kesa - 6 years, 10 months ago

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"He wants a 100 percent chance of getting a pair." Is that the clarification you want?

bj prognome - 6 years, 10 months ago

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@Bj Prognome – How about a pair of left and right?

Sharky Kesa - 6 years, 10 months ago

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@Sharky Kesa – I fixed it. Is it clearer now?

bj prognome - 6 years, 10 months ago

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@Bj Prognome – Not really, you want a pair of left and right gloves of the same colour.

Sharky Kesa - 6 years, 10 months ago

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@Sharky Kesa – "He doesn't care whether it's a blue pair or a white pair, and the gloves can be different colours. " says he doesn't care if the gloves are different colors.

bj prognome - 6 years, 10 months ago

I got this right but I was hesitating between 13 and 2. The thing that makes the question unclear is that in order to distinguish left/right glove you don't need light - you can distinguish them even in darkness (as anyone who has ever put opposite-side glove on can tell :)

To make the question entirely clear I would add two assumptions: 1) A pair of gloves is made of one left and one right glove 2) Sam is not able to distinguish left glove from right glove in the darkness.

Jan Hrček - 6 years ago
Chew-Seong Cheong
Aug 12, 2014

The worse possible case is Sam gets all gloves of one side (only left or only right). There are at most 12 gloves of either side, so if he grabs 13 gloves, he is 100 percent sure that he will get a pair.

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