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Posers and Puzzles

Posers and Puzzles

  1. Standard member talzamir
    Art, not a Toil
    09 Nov '11 14:07
    (This one I found online at one point and liked it. A slight rewording.)

    Adam and Ann organize a party for couples. They invite Bob and Beatrice, Cathy and Charlie, Dan and Doris.. all the way to Zebb and Zaltana. Every invited couple is somehow known to Adam and Ann, that is, there are no couples invited of whom neither Ann nor Adam would know neither the husband nor the wife.

    During the party, everyone mingles and exchanges calling cards with everyone they did not know before.. no one needs to exchange a card with his or her spouse. In the end, Ann asks how many calling cards everyone got, and hears to her surprise everyone Ann speaks with got a different number of cards.

    How many cards did Ann get? How about Adam?
  2. 10 Nov '11 14:08
    25?
  3. Standard member talzamir
    Art, not a Toil
    10 Nov '11 14:14
    Correct for Ann. How about Adam?
  4. 10 Nov '11 15:17
    Originally posted by talzamir
    Correct for Ann. How about Adam?
    Oh, no idea for adam
  5. Standard member talzamir
    Art, not a Toil
    10 Nov '11 18:27
    There are 52 people. No one gives himself or herself, or hir spouse a calling cards, so everyone can give up to 50 cards. That's 51 possibilities, and there are 51 people Ann asks, so they have given 0, 1, 2, ... 50 cards.

    Adam is not the person who exchange 50 cards, because if he did, then someone would have exchanged a card with him, and the zero can't be placed on anyone. The only way for there to be a person who exchanged 50 cards and for a person to have exchanged zero cards means that they are a couple. Say, Mr and Mrs Z.

    The only way for someone to have 49 cards, and just one, is that they are a couple. One of them gave to everyone except one of the Z couple, and one received a card from everyone except one of the Z couple. Say, Mr and Mrs Y.

    Repeat for another couple, 48 and 2. then 47 and 3. etc etc etc. Until Mr and Mrs B exchange 24 and 26 cards.

    Adam and Ann have received one card each from every invited couple; 25 cards each.