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Knights on the move


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11 replies to this topic

#1 bonanova

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Posted 12 May 2012 - 05:53 AM

This puzzle reportedly dates from the 13th century. So some of you older (ahem) Denizens may have encountered it already. Anticipating this possibility, I've added a competitive wrinkle to the mix.

On a 3x3 chessboard you are to place a knight on an unoccupied square and then move it to another unoccupied square using a legal knight's move. If you alternate turns with an opponent, the board eventually fills up to a point where there are not sufficient unoccupied squares for one of the players to complete a turn. The player who has that turn then loses the game. I.e., the last player to successfully complete a turn is the winner.

If first player is A and second player is B, which player wins the game if

1, Players cooperate to maximize the number of turns.
2. Players compete to win the game?

If you wish to describe a sequence of moves in your answer, it may be helpful to number the squares row-wise left to right starting with the top row

1 2 3
4 5 6
7 8 9

A legal move would then be 1 - 6, for example, provided that quares 1 and 6 are unoccupied prior to the move. Square 6 would remain occupied. Assume there are enough knights available to each player.
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#2 Thalia

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Posted 12 May 2012 - 06:56 AM

Spoiler for Non competitive

Spoiler for Competitive

Edited by Thalia, 12 May 2012 - 07:02 AM.

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#3 Aaryan

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Posted 12 May 2012 - 02:06 PM

Spoiler for

Edited by Aaryan, 12 May 2012 - 02:07 PM.

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#4 Aaryan

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Posted 12 May 2012 - 02:55 PM

Oh, I misunderstood the OP. So it's NOT the same knight moving around the squares?
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#5 bonanova

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Posted 13 May 2012 - 03:21 AM

Oh, I misunderstood the OP. So it's NOT the same knight moving around the squares?


Correct.

Each play leaves another knight on the board.
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#6 bonanova

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Posted 13 May 2012 - 03:22 AM

Spoiler for Non competitive

Spoiler for Competitive


Nice.

But you can do better on part 1.
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#7 Molly Mae

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Posted 14 May 2012 - 06:06 PM

Spoiler for If I understand correctly

Edited by Molly Mae, 14 May 2012 - 06:15 PM.

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#8 bonanova

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Posted 14 May 2012 - 06:38 PM

Spoiler for If I understand correctly


That's it, and very nice explanation.
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#9 bonanova

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Posted 14 May 2012 - 06:42 PM

Spoiler for Non competitive

Spoiler for Competitive


The second question was aimed at who would win if played competitively.
Is your "minimum" solution a statement that B wins if the players compete?
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#10 Thalia

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Posted 14 May 2012 - 06:48 PM

The second question was aimed at who would win if played competitively.
Is your "minimum" solution a statement that B wins if the players compete?

Spoiler for

Edited by Thalia, 14 May 2012 - 06:48 PM.

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