Editing 832: Tic-Tac-Toe
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| date = December 10, 2010 | | date = December 10, 2010 | ||
| title = Tic-Tac-Toe | | title = Tic-Tac-Toe | ||
− | | image = | + | | image = Tic_tac_toe.png |
| titletext = The only winning move is to play, perfectly, waiting for your opponent to make a mistake. | | titletext = The only winning move is to play, perfectly, waiting for your opponent to make a mistake. | ||
}} | }} | ||
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==Explanation== | ==Explanation== | ||
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1|2|3 | 1|2|3 | ||
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+ | Pixel values are taken from http://xkcd.com/832_large/. | ||
Each map shows every possible combination of moves which will result in that side winning or tying. It assumes that X moves first, and its optimal move is X7. Any corner would do, so X1, X3 and X9 are also optimal moves. The map for X has a big red X7 (650×650 pixels), and the 8 remaining grids have a smaller (210×210) black X7. | Each map shows every possible combination of moves which will result in that side winning or tying. It assumes that X moves first, and its optimal move is X7. Any corner would do, so X1, X3 and X9 are also optimal moves. The map for X has a big red X7 (650×650 pixels), and the 8 remaining grids have a smaller (210×210) black X7. | ||
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Note that only optimal moves are shown. For example, you can't find a grid beginning with X2 in Map of X, because X2 is not an optimal move. | Note that only optimal moves are shown. For example, you can't find a grid beginning with X2 in Map of X, because X2 is not an optimal move. | ||
− | In map for O you can find a 660×660 grid | + | In map for O you can find a 660×660 grid beginnig with X2. Since the optimal answer is O5, you won't find X2, O8, for example. |
;Example 1 | ;Example 1 | ||
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==Errors== | ==Errors== | ||
− | + | In Map for X, the grid for X7, O9, X1, O4, X3 (i.e. go to Map for X, select cell 9, and then select cell 4) shows the same picture for O5 and O6. Those pictures belong to O6. The correct pictures should be: | |
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− | The correct pictures should be: | ||
X| |O X| |O | X| |O X| |O | ||
-+-+- -+-+- | -+-+- -+-+- | ||
O|O| O| |O | O|O| O| |O | ||
-+-+- -+-+- | -+-+- -+-+- | ||
− | X| | + | X|X|X X|X|X |
− | + | In Map for X, the grid for X7, O1, X9, O8, X3 (i.e. go to Map for X, select cell 1, and then select cell 8) shows the same picture for O2 and O5. Those pictures belong to O2. The correct pictures should be: | |
X|O|X | X|O|X | ||
-+-+- | -+-+- | ||
Line 95: | Line 91: | ||
O|O|X | O|O|X | ||
− | + | In Map for O, the grid for X8, O5, X2, O6 (i.e. go to Map for O, select cell 8, and then select cell 2) shows the same picture for X1 and X3. Those pictures belong to X3. The correct pictures should be: | |
|X| \ / |X| | |X| \ / |X| | ||
-+-+- \ / -+-+- | -+-+- \ / -+-+- | ||
Line 102: | Line 98: | ||
X| |X / \ |X|X | X| |X / \ |X|X | ||
− | + | In Map for O, the grid for X2, O5, X8, O4 (i.e. go to Map for O, select cell 2, and then select cell 8) shows the same picture for X7 and X9. Those pictures belong to X7. The correct pictures should be: | |
X|X| \ / |X|X | X|X| \ / |X|X | ||
-+-+- \ / -+-+- | -+-+- \ / -+-+- | ||
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|X| / \ |X| | |X| / \ |X| | ||
− | + | In Map for O, the grid for X6, O5, X4, O2 (i.e. go to Map for O, select cell 6, and then select cell 4) shows the same picture for X1 and X7. Those pictures belong to X1. The correct pictures should be: | |
− | + | X|O| | |
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− | The correct pictures should be: | ||
− | X| | ||
-+-+- | -+-+- | ||
X|O|X | X|O|X | ||
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/ \ | / \ | ||
===== | ===== | ||
− | | | + | |O| |
-+-+- | -+-+- | ||
X|O|X | X|O|X | ||
-+-+- | -+-+- | ||
X|O| | X|O| | ||
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==See also== | ==See also== |