prove that no matter how you tile a 6 x 6 board using 2 x 1 tiles, there would always be a vertical or horizontal line separating the board. Separation here means that no tile would be cutting across that line

  • $\begingroup$ @JaapScherphuis Thanks for your comment. Indeed, both the questions are same. However, I am not able to understand the answer completely. Why would parity dictate that there has to be two bridging dominoes for every pair of adjacent rows/columns $\endgroup$ Aug 24, 2022 at 15:19
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    $\begingroup$ Every cutting lines splits it into two even areas. If only one domino bridged the line, it would leave an odd area on each side, and that odd area would have to be covered by dominos, and this is not possible. $\endgroup$ Aug 24, 2022 at 15:22


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