There is a 7-by-7 square grid containing an "A" and "B" in each square, in a checkerboard pattern. You must get the board to have no palindromes in it, going horizontally or vertically, in a full row or column.

Starting Grid:

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The goal is to find the least amount of turns needed to get no palindromes in a full row or column. Start with the starting grid. Then switch two squares that are right next to each other. Each switch you make counts as one turn.

Explain Your Reasoning


The minimum is five. There are fourteen palindromes in the grid. Each swap touches three, so we must have at least five. One of many ways to achieve that is to swap $(1,1)\leftrightarrow (1,2),(2,3)\leftrightarrow (2,4),(3,5)\leftrightarrow (3,6),(4,7)\leftrightarrow (5,7),(6,7)\leftrightarrow (7,7)$

  • $\begingroup$ Congrtraz! Good job! :) $\endgroup$ – Xandawesome May 28 '15 at 4:25

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