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After each of 50 cards is marked with a different whole number from 1 through 50, the cards are the paired at random. At most how many of these 25 pairs have a sum of 25?

 Feb 8, 2020
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Well, you should have: 50C2 =1,225 ways of pairing those 50 numbers. But only 12 pairs sum up to 25. Technically, there should be 12 x 2 = 24 pairs if the cards are DISTINCT such as different-colored cards, or cards of different shapes and sizes....etc. To my understanding, then you should have at most 24 pairs that sum up to 25:

 

Such as: 24 + 1, 23 +2, 22 + 3, 21 + 4, 20 +5......etc. And if they are DISTINCT, then: 1 + 24, 2 + 23, 3 + 22, 4 + 21, 5 + 20........and so on.

Note: Somebody should check this. Thanks.

 Feb 8, 2020

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