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Poker Chip Puzzle

  1. Nov 21, 2005 #1
    There is a full story that comes along with this puzzle but I will just stick to the puzzle itself.

    There are four men. Three of them are friends and the fourth has approached them with a proposition for a bet which they have taken him up on. We'll call the three friends Bob, Tom, and Jim. We'll call the fourth man, who has proposed the bet, Mr. Chip.

    The Bet: Mr Chip will hold out a bag containing five poker chips, two are red and three are black. Each of the three friends will remove one poker chip from the bag without looking at the chip they have removed keeping it completely concealed in their hand. Each of the three men in turn will have an opportunity to see what colour chips his two friends have (the friends will show their own chips without looking at the chips themselves) and an opportunity to tell Mr Chip what colour chip he holds in his own hand (the observers hand, not Mr Chip's hand, Mr. Chip is not holding a chip). If the observer tells Mr. Chip the right colour of the chip in his hand the three men win the bet. If the observer fails to tell Mr. Chip the right colour the three men automatically lose the bet. For this reason they have the option to abstain from answering and allow the next to take his turn. Each man gets only one turn. Only one man needs to answer correctly for the three to win the bet and only one needs to answer incorrectly for the three to lose the bet.

    What happened: Each of the three friends took one chip from the bag. Bob decided to take his turn first. He looked at his friends' chips and decided he was unable to determine what colour chip he had in his hand so obstained. Tom then took his turn looking at his friends' chips and also decided that he could not decide what colour chip he possessed in his hand so abstained.
    When Jim's turn came he stopped his friends from showing him their chips and told Mr. Chip that he would like to double the bet and tell Mr Chip what colour chip is in his hand with out looking at his friends's chips.

    The Puzzle Question: Jim has not cheated in any way shape or form nor has he made any guesses. Jim has logically deduced the colour of the chip in his hand. What colour is the chip in Jim's hand and can you describe the process of deduction Jim used to determine the colour of the chip?
  2. jcsd
  3. Nov 22, 2005 #2
    if bob saw two reds, he'd've known he was black, therefore jim and tom cannot both have red. If tom realizes this, then he looks at jims. if jims is red, then tom's must be black since one of them has to be. since tom isn't sure what he has, this means that jim must have black. which jim can deduce without ever seeing the others.
    Last edited: Nov 22, 2005
  4. Nov 22, 2005 #3
    Hooray for Gale!
    I had hoped people would find it a bit more difficult though.
  5. Nov 22, 2005 #4
    sorry.... it was difficult!
  6. Nov 22, 2005 #5
    Lol... thank you Gale. :approve:

    It's also good to know that pretty ladies can work logic puzzles. Too bad I've never met one in real life.:frown:
  7. Nov 24, 2005 #6
    Someone didn't make a good bet! They can win with any configuration right?
  8. Nov 25, 2005 #7
    As long as the "guessers" know what they are doing and can rely on each other to make the correct choices they should be able to win no matter what.


    And as long as Mr. Chip doesn't somehow cheat ofcourse.
  9. Dec 4, 2005 #8
    I love this riddle. I heard a different variation of it but I loved solving it. I was very happy when I finally did it :)
  10. Dec 5, 2005 #9
    Yes, but the point is Jim won't get to play (or double the bet) if he has red. That how he knows he has black without looking if the turn gets to him.
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