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        riddles >> easy >> Knight’s move and original position puzzle
        
(Message started by: K Sengupta on Jan 16^th, 2010, 12:24am)

Title: Knight’s move and original position puzzle
Post by K Sengupta on Jan 16^th, 2010, 12:24am

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?

Title: Re: Knight’s move and original position puzzle
Post by MathsForFun on Jan 16^th, 2010, 12:44am

on 01/16/10 at 00:24:31, 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?

This example solution, on board {a..d}{1..3}, entails visiting some squares more than once (which is not forbidden in the question):

[hide]a1 c2 a3 b1 c3 d1 b2 d3 c1 b3 d2 b3 (second visit) c1 (second visit) a2[/hide]

Title: Re: Knight’s move and original position puzzle
Post by Obob on Jan 16^th, 2010, 1:35am

Landing on squares more than once is implicitly forbidden.

Title: Re: Knight’s move and original position puzzle
Post by towr on Jan 16^th, 2010, 4:43am

[hide]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.[/hide]