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## Main Question or Discussion Point

I was doing a brain treaser where the letters A-H had to be put into an array 2 by 4 such that no letter is adjacent or diagonal to a letter one unit different. That is a C can't be above, below, to one side of, or diagonal from a B or D. I solved the problem but the thought occured to me that using modular logic it can easily be proven that the H has to be above,below,to one side of, or diagonal to the A. In other words, it is immposible to put the numbers 1-8 into an 2 by 4 square box array, such that where each every set of boxes that touch either by a side

or corner the difference between the 2 boxes mod 8 is more than 1. Does any one care to give a simple proof?

or corner the difference between the 2 boxes mod 8 is more than 1. Does any one care to give a simple proof?