Quantum Tic-Tac-Toe

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This Month’s Challenge: December 2004

Running it in Reverse

This month's challenge is the sixteenth that we've published. My thanks to all of you who have read and tried these puzzles, and my special thanks to Peter Schueller and Nathan Conley, who sent their solutions to some of the puzzles.

Up to now, I've already had the answer to a puzzle when I publish it. Not this time. The inventor of the game came to me a couple of days ago, with this challenge: We know that any quantum game corresponds to an ensemble of classical games. But does every ensemble of classical games, correspond to a quantum game?

In other words, can you construct an ensemble of classical tic-tac-toe games, that does not correspond to a Quantum Tic-Tac-Toe game? Such an ensemble has to consist of legal tic-tac-toe games, with the same number of X's and O's in each game.

Good luck to all of us. I wonder if I'll receive something from one of you, before I've found one myself. Allan assures me it can be done.


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: November 2004
Doom?

Last month we presented two similar puzzles. In both of them, all marks are real, and X has real marks in three corners of the board. In one game, it is O's turn, in the other it is X's, and the challenge is whether O can pull off a win in either game.


Move X O
1 1 - 9 1< 9
3 3 - 6 6 - 7
5 7< 3 ?
7 5 - 8  
9    
  
I made a mistake last month. Move 2 was written incorrectly. I typed move 2 as "1>9" indicating that the ghost "O" in square 9 should become real, and it should have been "1< 9" (the ghost "O" in square 1 becomes real). My apologies. The mistake is corrected here.
In this puzzle, O cannot win, unless X is not paying attention at all. No matter what O does for move 6, X needs merely place his marks in squares 5 and 8 for move 7. He is then guaranteed a win on move 7 whenever the final collapse happens, while O cannot possibly construct a win earlier than move 8.

Move X O
1 1 - 3 5 - 9
3 1< 3 5 >9
5 7 - 8 7 >8
7 2 - 4  
9    
  
 
In this puzzle, the situation is similar; X will win if he places his marks in squares 2 and 4, regardless of what O does.

Even in Quantum Tic-Tac-Toe, whoever has three corners, has the game.

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