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Imagine a chess piece (we'll call it the "majarajah") that combines the powers of the queen and the knight. The task is to place ten majarajahs on a 10x10 chessboard so that none of them are attacking each other.

To illustrate the problem, here are two positions that don't quite fulfill the requirements. In the first position, the majarajah on the left edge attacks another majarajah by a knight move. In the second position, the majarajah on the left edge attacks another majarajah along a diagonal.

_ _ _ X _ _ _ _ _ _
_ _ _ _ _ _ X _ _ _
_ _ _ _ _ _ _ _ _ X
_ X _ _ _ _ _ _ _ _
_ _ _ _ X _ _ _ _ _
_ _ _ _ _ _ _ X _ _
X _ _ _ _ _ _ _ _ _
_ _ X _ _ _ _ _ _ _
_ _ _ _ _ X _ _ _ _
_ _ _ _ _ _ _ _ X _


_ _ _ _ X _ _ _ _ _
_ _ _ _ _ _ _ _ X _
_ X _ _ _ _ _ _ _ _
_ _ _ _ _ X _ _ _ _
_ _ _ _ _ _ _ _ _ X
_ _ X _ _ _ _ _ _ _
_ _ _ _ _ _ X _ _ _
X _ _ _ _ _ _ _ _ _
_ _ _ X _ _ _ _ _ _
_ _ _ _ _ _ _ X _ _

2007-01-31 11:26:11 · 2 answers · asked by Anonymous in Science & Mathematics Mathematics

Not quite, Lizzy... two pairs of majarajahs attack each other along diagonals.

I've had a couple of folks express interest about this puzzle, so I've extended the deadline. Yeh, it's tough - not counting reflections and rotations, there is only one solution!)

2007-02-02 13:08:31 · update #1

2 answers

This looked really hard at first. Then I noticed in your second example of a wrong solution, if the maharajah on the far left is moved all the way to the right, he doesn't attack anybody. To get an answer then, move all the maharajahs to the left one space and have the maharajah on the far left wrap around to the far right.

_ _ _ X _ _ _ _ _ _
_ _ _ _ _ _ _ X _ _
X _ _ _ _ _ _ _ _ _
_ _ _ _ X _ _ _ _ _
_ _ _ _ _ _ _ _ X _
_ X _ _ _ _ _ _ _ _
_ _ _ _ _ X _ _ _ _
_ _ _ _ _ _ _ _ _ X
_ _ X _ _ _ _ _ _ _
_ _ _ _ _ _ X _ _ _

Nice pattern! Is that really the only answer?

2007-02-04 04:43:18 · answer #1 · answered by obit17 2 · 0 0

X _ _ _ _ _ _ _ _ _
_ _ _ X _ _ _ _ _ _
_ _ _ _ _ _ X _ _ _
_ _ _ _ _ _ _ _ _ X
_ X _ _ _ _ _ _ _ _
_ _ _ _ X _ _ _ _ _
_ _ _ _ _ _ _ X _ _
_ _ X _ _ _ _ _ _ _
_ _ _ _ _ X _ _ _ _
_ _ _ _ _ _ _ _ X _

2007-02-02 15:10:49 · answer #2 · answered by lizzy208_ayla 2 · 0 0

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