This is an entry for the 17th Fortnightly Challenge.


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


It is not possible.


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.

  • $\begingroup$ How If he start from (1,2) cell (2nd top left), is it possible? $\endgroup$ – Jamal Senjaya Oct 5 '16 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 '16 at 5:46

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