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Topic: need help with penny track game (Read 4097 times) |
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priyagopi76
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need help with penny track game
« on: Aug 24th, 2004, 9:26pm » |
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Can I get some hint on solving the penny track game?
There are three one-dimensional tracks, of length 12, 7, and 5 spaces respectively. You start with pennies in the first space of each track; your opponent starts with pennies in the last space of each track. On your turn, you may move any one of your pennies any number of spaces in either direction along a track (as a chess rook), however you are not permitted to bypass the other player's penny or occupy its space. If a player has no legal move, he loses.
What should your first move be?
Thanks
Priya
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rmsgrey
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Re: need help with penny track game
« Reply #1 on: Aug 25th, 2004, 5:48am » |
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This is a thinly disguised version of one of the Nim-like puzzles. If you look in the Easy forum for a thread with the word "pearl" in the title you should (if memory serves) find a general solution.
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Ladadadada
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Re: need help with penny track game
« Reply #2 on: Oct 21st, 2008, 7:21pm » |
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I must be confused about how this game works because I can't see any challenge at all in winning if you go first.
I have to assume that when the puzzle said "move any one of your pennies any number of spaces" that zero spaces was not allowed. Otherwise the game would always end in a stalemate with both players having legal moves and neither player willing to give up any ground. In fact, even a trapped penny would still have a legal move of moving zero spaces.
Here is the opening position with my penny (M) in the first space and his penny (H) in the last space of each track.
|M| | | | | | | | | | |H|
|M| | | | | |H|
|M| | | |H|
For my first move I move my penny as far as I can on the longest track.
| | | | | | | | | | |M|H|
|M| | | | | |H|
|M| | | |H|
For his first move he will (presumably) move his penny as far as he can on the second longest track.
| | | | | | | | | | |M|H|
|M|H| | | | | |
|M| | | |H|
And following this I move my third penny to the far end of the remaining track.
| | | | | | | | | | |M|H|
|M|H| | | | | |
| | | |M|H|
Now he only has one penny that has a legal move. He must move it at least one space. No matter how far he moves his penny I will move my penny as far as I can on the same track leaving him only one legal move again until he ends up at the far end of the track and has no legal moves left.
Have I completely misinterpreted the rules of the game or is it really that simple ?
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Grimbal
wu::riddles Moderator
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Re: need help with penny track game
« Reply #3 on: Oct 22nd, 2008, 12:30am » |
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If you do
| | | | | | | | | | |M|H|
|M| | | | | |H|
|M| | | |H|
I do
| | | | | | | | | | |M|H|
|M| | | |H| | |
|M| | | |H|
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