Theophilos S.

asked • 03/05/15

6 different pairs of winter shoes and 8 different pairs of summer shoes How can be certain he has a pair of matching winter shoes?

need to solve this problem.

1 Expert Answer

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Arthur D. answered • 03/05/15

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assuming he picks out one shoe at a time
he could pick all 8 pairs of summer shoes, one shoe at a time before he starts picking winter shoes
that's 16 picks for the 8 pairs of summer shoes
suppose the winter shoes are...
AA, BB, CC, DD, EE, FF
he could pick A, then B, then C, then D, then E, and then F for 6 more picks for a total of 16+6=22 picks and not have a pair of matching winter shoes
on the next pick, the 23rd pick, he has to pick one of the shoes that is left...
he picks either A, B, C, D, E, or F and has a matching pair, again on the 23rd pick to be certain that he has a pair of matching winter shoes
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