QT3 - This Month's Challenge

This Month’s Challenge:

July 2004

A Quantum Game without a Classical Game

In the metaphor that Quantum Tic-Tac-Toe supplies to quantum physics we have argued that every completed quantum game implies a classical game. This is strictly true only for games that go through all 9 moves. Find an example of a quantum game that ends in a win where there is not an equivalent classical game.

Be sure to include your name and email address! We want to give credit to the person that sends the best solution.

Email your solution to support@NovatiaInc.com!

Last Month’s Answer:

June 2004

Widest Point Spread in a Collapse

Last month's challenge was to find quantum game that wasn't decided until the last move, with X winning if the choice went one way and O winning if it went the other, and with the widest possible point spread between X's win and O's win.

There's several solutions to this problem, including one that's quite pretty. But first, we apologize for including a "red herring" in the challenge; it is not possible for O to win by two points. To do that, she'd have to make two intersecting lines, and that takes five marks, and she can only put four marks on the board.

Here's one solution:

Move X O

1 1 - 3 7 - 5

3 4 - 8 5 - 3

5 9 - 8 6 - 2

7 7 - 9 6 - 5

9 7 ? 2

Analysis of game

As a game, this is weak. It's purely constructed to solve the challenge. Both players cooperate to lay out their three-rows, X down one side and across the bottom, and O along a diagonal, without getting each in the other's way. At the ninth move, O gets to choose whether X's last move will be in square 7 or square 2. If the last X mark goes in square 7, X wins by 2 points; if it goes in square 2, O wins by 1 point.

This solution is much better; it is a better game and it is prettier at the end:

Move	X	O
1	1 - 3	3 - 2
3	8 - 1	5 - 4
5	4 - 7	7 - 6
7	6 - 9	9 - 8
9	2 ? 5

Analysis of game

X lays claim to the top row.
O counters, so that X cannot make a 3-row along the top.
X makes a knight's move.
O begins to lay claim to the middle row.
X moves into the left column and the bottom row, and threatens the middle row.
O's knight's move limits X's threats to the middle row and the diagonal.
X threatens to make a 3-row down the right side and along the bottom. At this point, the ensemble contains 20 classical games; X has a win across the bottom in 6 of them, and O has a win on the diagonal in 2 of them.
O moves in the bottom row, reducing the ensemble to 9 classical games and eliminating all of X's wins, while giving herself 5 wins (the diagonal in one classical game, and the middle column in 4 others).
X counters O's threat in the middle column, reducing the ensemble to just 2 games, in one of which he wins big.

O gets to choose which of those final two classical games, actually becomes real, and thus whether she wins on one diagonal, or X wins on both diagonals for two points.