Find a connected arrangement of squares such that it is not possible to tile it with 2x1 dominoes, but if you increase the shape by adding a 2x1 shape to it, you can now tile the new shape with 2x1 dominoes.Naturally, I mean 'tile' in the sense of the domino problem. Note that the solution to this problem requires a connected shape. I hope I don't need to define connected, I mean, I could, but its annoying.
Covering Problem
As promised, the follow up problem:
Covering Solution
Alright, I'm pretty sure I still have this blog, and now I have something of a backlog of puzzles to post. Something of an embarrassment of riches that I don't bother to post as often as I learn new puzzles, but thats life I guess. Anyway, time for the solution to the domino problem from last time.
The solution is very simple: Consider naming the squares on the chessboard black and white, with no two of the same colour adjacent (the way chessboards are actually coloured). A given domino must cover exactly 1 white and 1 black square. The standard chessboard has 32 squares of each colour, but opposite corners are always the same colour so removing two of opposite corners will leave us with 32 squares of one colour and 30 of the other. It will not be possible to cover this with 31 dominoes.
Thats it really, I'll follow this with a post about the follow up problem.
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