Here is a problem quoted from fakalin. A full deck of cards has 52 cards. Suppose 10 of them were face up and 42 were face down. You are in a dark room holding the deck. How do you rearrange the deck into two subdecks so that they have the same number of cards facing up?
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It is said that 8 perfect shuffles of a standard deck of 52 cards results in an unshuffled deck. Why is that? Is it true only for 52 cards? What kind of shuffle is implied by this statement? Yesterday, we (high school math buddies) made pretty good sense of it.
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