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Old 02-08-2018, 03:33 PM
fiddleback fiddleback is online now
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Join Date: May 2013
Posts: 10
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Quote:
Note that two clicks on any tile (on, then off again) maintains the same state. So any odd number in your solution matrix becomes a 1, and any even number becomes a 0. To solve your puzzle, click the ones.
I'll clear this up a bit: Clicking a single tile 2, 4, 6, or 8... times has the same effect on the surrounding eight squares as not having clicked it at all, regardless of what other tiles may have been clicked. Clicking a single tile 3,5,7, or 9... times has the same effect as clicking it once, again regardless of what other tiles may have been clicked.

When you add up the solutions from individual lit tiles, your matrix might look something like this. (Of course, it should be 5x7. I'm using 3x3 to demonstrate.):
Code:
3 0 1
2 6 8
1 5 4
Clicking the counts in the above solution will result in the same final board state as clicking the counts below:
Code:
1 0 1
0 0 0
1 1 0
Why? Because clicking any square a second time completely cancels any changes that resulted from clicking it once. Clicking any square more than once is unnecessary.

My only doubts in the approach I've posted hinge on whether or not it's actually possible to solve a board with a particular single tile illuminated. If not, things will be a bit trickier.
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