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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)

Comments: ( Back to comment list | You must be logged in to post comments.)
One (long) example of play. | Comment 3 of 5 |
1 1 P 1 points at P 2's right hand 11 1 P 2's right hand has two, and is pointed at 1's right 111 1 P 1 points his right hand at P 2's right hand 0 1 P 2 has one fist. He cannot point to his own hand to eliminte the fist, as his left only has 1. He points his left at P 1's right if he is not too bright. 1111 1 P 1's right has four, so he points it at P 2's left 0 0 P 2's left is a fist, so he loses If P2 was cleverer at stage 4, stages 4+ might be like this: 0 1 P2 points at P 1's left 111 11 P 1 points his left at P2's left 0 111 P2 cannot win, as whichever hand he points to on P1 will still leave the enough with enough to fist him, so he points it at his own. 1 11 111 11 P1 points at P2's left (11) with his right (111), reducing it to a fist 1 0 P2 Points at P1's left 111 111 P1 points at P2 1111 0 P2 has to point at his own fist to survive. 11 11 111 111 P1 points at P2 0 11. P2 points at his own fist. 1 1 etc. So it might be a slight advantage to be P1, as you can reduce the opponent guicker. One strategy might be to spread the pointing, the reduce the opponents's "damage" as he hits you.
  Posted by Jake on 2004-07-16 09:22:57
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