|
Last month, you were given two similar games, in progress.
You were asked whether X could win them both,
whether he could win by move 5,
and whether O could get a point also.
You were also asked if you could devise a quantum setup that
could yield both games.
|
|
|
|
The game setup is actually the harder part of the problem;
let us do that first.
We want a situation where, when the collapse happens,
a real X and O are in two corner squares in both realities,
and where another real X and O swap corner squares in the two realities.
To the right, is that game just before the collapse.
The classical ensemble shows the two possible collapses.
In both cases, X can win, and he can win by move 5
(although the game will proceed to move 6 or 7,
in order to set up the collapse that gives him the win on move 5).
In one case, O will get no point; in the other, she can get a half-point.
If X chooses the collapse that gives him real Xs in squares
3 and 7,
then move 5 must be in the center and any side (it doesn't matter which).
O will either echo his move, giving him the choice on the next collapse,
or she will do something different,
in which case he will repeat move 7 in the same squares as move 5,
giving O no choice about the collapse. Either way, he chooses to
reify move 5 in the center, and he wins.
If X chooses the collapse that gives him real Xs in squares 3 and 9,
then move 5 must be in squares 4 and 6.
Again O can echo his move, and he chooses the collapse,
or she can do something different and he will place move 7 in squares 4 and 6 again.
But if O does place move 6 in squares 4 and 6, she will get a half-point
because she will have a 3-row down the left column; if she does something
else, she will end the game with nothing.
|
|
|