• Cards
• Objective
• Play
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The Transposition game uses an even number of cards numbered 1 through N, where N is at least 8.

The game begins with the cards arranged in increasing order, from left to right:

The first player wins if the odd numbered cards are arranged in decreasing order from left to right, but not necessarily consecutively.

The second player wins if the even numbered cards are arranged in the same manner.

It doesn't matter which player actually arranges the cards in the required order. I.e. if after some move the odd numbered cards are arranged in the required order then the first player wins, even if the cards were arranged by the second player.

If both odd and even numbered cards are arranged simultaneously (i.e. by the same move) then the game ends up in a tie.

Players move alternatively, passing is not allowed.

On his turn, a player must switch any two cards such that the left card has a smaller number than the right card.

The pie rule is used for making the game fair. This rule allows the second player to switch places after the first player makes his first move.

• Only the adjacent cards can be switched
• The first player wins if the cards numbered from 1 to N/2 are arranged in decreasing order from left to right and the second player wins if the cards numbered from N/2 + 1 to N are arranged in the same manner (instead of arranging odd and even numbers).

• Transposition rules on "Cut-the-Knot" site.