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Fingers game (Posted on 2004-07-11) Difficulty: 4 of 5
The fingers game is quite simple, and can be played anywhere with another person.

1. The two players start by holding up two fingers each, one on each hand.

2. On a player's turn, that player can point with one hand to any of the three hands around him (his own or the other players'). The hand that gets pointed to adds the number of fingers on the hand that did the pointing to his own, and sticks that many fingers up. For instance, if my right hand has two fingers up and I point it to your left hand, which has one finger up, you would now show three fingers on your left hand.

3. If five fingers or more should be up, make a fist. A fist cannot be used to point with.

4. If you have one fist and your other hand has an even number of fingers, you can point with the second hand to the fist on your turn, and divide the fingers evenly between the hands. This is the only time a fist may be pointed to.

Players alternate turns, and the first player to show two fists loses.

Is there a winning strategy for either player? Which player, if either, has a better chance of winning?

No Solution Yet Submitted by Sam    
Rating: 4.0000 (4 votes)

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Solution simple display of solution Comment 5 of 5 |

I am going to show you the simplest way of proving that Player one, the first player to point and add fingers to Player two's hand, if he is trying, will win the game.

|= fingers, O=fists

A= right hand, B= left hand

Player one goes first.

Score-  Player one-  A |   B |

           Player two-  A |   B |

1st turn- Player one uses hand A to point to Player two's hand B.

Player one-  A |   B |

Player two-  A |   B ||

2nd turn- Player two uses hand B to point to Player one's hand A.

Player one- A |||   B |

Player two- A |   B ||

3rd turn- Player one uses hand A to point to Player two's hand B, Player two now has one fist.

Player one- A |||   B |

Player two- A |   B O

4th turn- Player two uses hand A to point to Player one's hand A

Player one- A ||||   B |

Player two- A |   B O

5th turn- Player one uses hand A to point to Player two's hand A, Player two now has two fists and loses the game with the results:

Player one- A ||||   B |

Player two- A O   B O

There are, of course, other strategies to beating Player two in this game. It is impossible for Player one to lose unless he is not trying.

--------Player one wins.----------






  Posted by James on 2005-08-23 04:43:12
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