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Topic: Help with a game called flip it! (Read 823 times) |
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uzo
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Help with a game called flip it!
« on: Feb 8th, 2008, 5:12am » |
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Hello, I am stucked with a game called flip it!. The purpose of this game is to flip all the pegs to the opposite side. The difficult part is that when you flip a peg, its surrounding pegs will also be flipped. I need the solution for a 10X10 game. Anyway, this is how far I get:
And here is the link to the game:
http://www.novelgames.com/flashgames/game.php?id=7
Any suggestions perhaps?
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Grimbal
wu::riddles Moderator
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Re: Help with a game called flip it!
« Reply #1 on: Feb 8th, 2008, 6:27am » |
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In the first row, click the 1st, 3rd, 8th and 10th.
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uzo
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Re: Help with a game called flip it!
« Reply #2 on: Feb 8th, 2008, 7:41am » |
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I don't quite understand. If I do what you suggested, I get this:
This doesn't help me much. Or did you mean something else?
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uzo
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Re: Help with a game called flip it!
« Reply #3 on: Feb 8th, 2008, 7:45am » |
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Already figured it out. Thank you very very much!
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FiBsTeR
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Re: Help with a game called flip it!
« Reply #4 on: Feb 8th, 2008, 8:27pm » |
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Interestingly enough, the solution for the 10x10 using your hint turns out to be exactly 100 moves.
Just out of curiosity, Grimbal, how did you figure that out? I have a similar game on my phone, except with a 5x5 board, and it took me two dedicated days to find a strategy guaranteed to win, so I'm wondering how you were able to find a solution on a 10x10 board in a little over an hour after uzo's post. 
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Eigenray
wu::riddles Moderator
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Re: Help with a game called flip it!
« Reply #5 on: Feb 8th, 2008, 9:36pm » |
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When a problem comes along, you must flip it. Isn't this just lights out? Think of it as a linear algebra problem. Try to detect it. It's not too late. To flip it. Flip it good.
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Grimbal
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Re: Help with a game called flip it!
« Reply #6 on: Feb 9th, 2008, 10:05am » |
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Nice avatar, Eigenray. 
There was a thread here about this problem already.
The idea is that once you know which cells from the top row you need to flip, then you have no choice for the remaining rows. The remaining cells from the 1st row tell you which cell to flip on the 2nd row, then the remaining cells on 2nd row tell you which cell to flip on the 3rd row, etc. So the big question is: which cell to flip from the 1st row.
In fact, for each way to flip cells on the top row, you will have some set of cells remaining on the last row. By flipping one cell on the top row, after clearing again the board down to the last row, you will see that it has changed some of the cells on the bottom row.
For each cell flipped on the top row, after clearing the picture down to the last row, a set of cells is flipped on the last row. If you flip a set of cells instead of individual cells, for each set of cells flipped on the top row, it results in a flip of a set of cells on the last row. And the relation is linear.
So you can play around with these sets and figure out which set of cell to flip on the top row to flip each cell individually on the last row. What you do, basically, is to find the inverse of a boolean matrix, and for that you can use Gaussian elimination.
When you know how to flip individual cells on the last row, you can combine the moves and find out how to clear the remaining cells on the last row.
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| « Last Edit: Feb 9th, 2008, 4:18pm by Grimbal » |
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jollytall
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Re: Help with a game called flip it!
« Reply #7 on: Mar 8th, 2008, 4:19am » |
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on Feb 8th, 2008, 8:27pm, FiBsTeR wrote:| Interestingly enough, the solution for the 10x10 using your hint turns out to be exactly 100 moves. |
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Why 100? It was 44 only to me.
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