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Topic: Knight’s move and original position puzzle (Read 526 times) |
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K Sengupta
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Knight’s move and original position puzzle
« on: Jan 16th, 2010, 12:24am » |
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Using knight’s move in a 3x4 chessboard, can a chess knight situated on any of the 12 squares, visit every other square and land back on its original position?
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MathsForFun
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Re: Knight’s move and original position puzzle
« Reply #1 on: Jan 16th, 2010, 12:44am » |
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on Jan 16th, 2010, 12:24am, K Sengupta wrote:| Using knight’s move in a 3x4 chessboard, can a chess knight situated on any of the 12 squares, visit every other square and land back on its original position? |
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This example solution, on board {a..d}{1..3}, entails visiting some squares more than once (which is not forbidden in the question):
a1 c2 a3 b1 c3 d1 b2 d3 c1 b3 d2 b3 (second visit) c1 (second visit) a2
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Obob
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Re: Knight’s move and original position puzzle
« Reply #2 on: Jan 16th, 2010, 1:35am » |
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Landing on squares more than once is implicitly forbidden.
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towr
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Re: Knight’s move and original position puzzle
« Reply #3 on: Jan 16th, 2010, 4:43am » |
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If you disentangle the graph, it's very easy to see you can't make a tour when you vist each square only once.
If you don't need to return to the square you start, there are 6 places where you can start such that you can visit the other 11 without visiting a square twice.
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