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This is an entry for the 17th Fortnightly Challenge.

A knight's tour is a sequence of moves of a knight on a chessboard such that the knight visits every square only once. If the knight ends on a square that is one knight's move from the beginning square (so that it could tour the board again immediately, following the same path), the tour is closed, otherwise it is open.

Jim tries to create a closed knight's tour on a 7x7 board from top left corner, is it possible ? If not Why?

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It is not possible.

Why?

Knight moves alternate between black and white squares. As the number of squares in a 7x7 board is odd, any open tour that starts in a black square ends in a black square, and the knight can only move to white squares after that, meaning he can't return to the square he started in to make it a closed tour.

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  • $\begingroup$ How If he start from (1,2) cell (2nd top left), is it possible? $\endgroup$
    – Jamal Senjaya
    Oct 5, 2016 at 5:42
  • $\begingroup$ Still not, if he starts from a white square, after an even number of moves he ends in white and can't return $\endgroup$
    – ffao
    Oct 5, 2016 at 5:46

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