Tuesday, January 21, 2020
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Card trick =_3

Vikas MyAiM proposed the following problem:

Say you are sitting in a dark room, where you are handed a deck of 52 cards. Ten of those cards have been turned facing up; the rest are facing down. Your job is to separate the cards into two stacks, each containing the same number of cards facing up.

Is it possible to do this? Marilyn vos Savant answered the question: “Yes, just deal yourself 10 cards and turn all of them over! Try it and see, readers.”

Mike Ecker explains: Say that N of the 10 cards that make up the second pile are already facing up before you turn the pile over. Then the other 10-N cards in this same pile are face down. Moreover, the first pile still has 10-N cards face up.

By now reversing the 10 cards you have dealt yourself, instead of N up and 10-N down, you now have 10-N face up — matching the 10-N face up in the first pile. Very clever and totally independent of where the 10 cards lie!

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