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Interference
Last month's challenge, without going into all the details,
was to devise two games that were similar,
and then superpose the two games to make a dissimilar game.
Here is the solution, in two parts.
First, the two similar games, showing O's best choice for move 4:
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| Game 1 |
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Game 2 |
X threatens to make three in a row in column 1, and win.
O's move blocks that, and builds some strength in column 3.
When we superpose the two games, a real mark in the same square in both games,
stays real;
a real mark in different squares in the two games,
becomes spooky marks in those squares in the superposed game.
X has a different threat in Game 3, and if he is not countered immediately,
he will move again in squares 4 and 7, and will win.
O must counter by moving in squares 4 and 7 herself.
So Game 3 looks like this:
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| Game 3 |
So, we superposed two games and got a game that develops quite differently.
There is a clear similarity between these games, and a situation in physics
called the double-slit experiment. In that experiment, a light is shone
through a pair of closely-spaced slits. If one slit or the other is blocked,
the light goes through the open slit and produces a diffraction pattern on
a screen (the light is brightest straight behind the slit,
and fades out to either side).
But if both slits are open, the light goes through both slits and interferes
with itself, producing a pattern of alternating bright and dark stripes on
the screen.
There are, in fact, places on the screen that are lit if one slit is closed,
that are dark if both slits are open.
Similarly, in the first two QT3 games shown here, one or the other of squares 4 and 7
are blocked by a real mark, and O has a 50/50 chance of ending up with move 4
in the rightmost column at the end of the game.
In Game 3, both squares 4 and 7 are open, and she has no chance at all
of move 4 being in the rightmost column.
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