Five-card magic trick

[Susam Pal]

Two mathematicians perform a trick with a shuffled deck of
distinct cards. One mathematician asks a member of the audience
to select five cards at random from the deck while the other
mathematician is blindfolded. The audience member hands the five
cards to the first mathematician who examines the cards, hands
one of them back to the audience member, arranges the remaining
four cards and places them face down into a neatly stacked pile
on a table. The audience member is then allowed to move the pile
on the table or change its orientation without disturbing the
order of the cards in the pile. The second mathematician now
removes his blindfold, examines the four cards on the table and
determines the card held by the audience member from these four
cards and their order in the pile.

If there were one more distinct card in the deck, the
mathematicians cannot perform this trick. How is this trick
done?

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Originally posted at: http://cotpi.com/p/44/

Solutions to 'Non-decimal square':
http://cotpi.com/p/43/#responses