Use of Several Grids in the Knight Tour’s Game to Find Shorter or Longer Biochemistry’s Sentences

Abstract

Knight tour is a mathematical problem that was first solved by Leonhard Euler (1707-1785). The problem consists in finding if it is possible that the knight piece of chess can tour through all the boxes of a chess grid, passing only once through each box. Bishop piece can only move to diagonal boxes of one color, and pawns can only move in one column. It can be easily seen that king, queen and rook can move through all the boxes. But it was not clear that the knight could move all through. Euler found several solutions for the 8x8 grid, and he numbered all the boxes of the grid in the order through which the knight passed. Surprisingly, he obtained some solutions with semi-magic squares, in which the sum of all the numbers of each row and column was the same. Nevertheless, diagonals didn’t sum the same, as happens in the magic squares. One of the typical games in word game’s books is the knight tour, with a 5x5 grid, that hides a 25-syllable sentence. The objective of this work was to study other grids, to obtain different sentences length with 3x3 (9-syllables), 4x4 (16-syllables), 5x5 (25 syllables), 6x6 (36 syllables) or 7x7 (49 syllables) grids. Thus, this game would be more versatile and could be used more extensively than limiting it to 25-syllable sentences.