Card Trick
by Ajay Kumar, Marilyn vos Savant, and Mike Ecker
Ajay Kumar 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!