MathDB
Funny movement, but no tour possible

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June 14, 2006
quadraticsmodular arithmetic

Problem Statement

Let PP and QQ be two horizontal neighbouring squares on a n×nn \times n chess board, PP on the left and QQ on the right. On the left square PP there is a stone that shall be moved around the board. The following moves are allowed: 1) move it one square upwards 2) move it one square to the right 3) move it one square down and one square to the left (diagonal movement) Example: you can get from e5e5 to f5f5, e6e6 and d4d4. Show that for no nn there is tour visting every square exactly once and ending in QQ.