The 2x2 case is impossible, I suspect it is related in some way.
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Seems this is related to Hamiltonian path problems. The issue is there is always one square that can’t be picked up. Why could this be?
I am afraid that I didn’t apply any rigor here and thought I solved it. Been playing with it for a bit and see there is likely not a solution. Good fun for me.
Rooks don’t move diagonal. I was able to do this exercise in my head on about the third try however. Start with big laps round the outside x2, then column by column to finish
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Let’s see it warm on a spoon and not get ahead of ourselves just yet :) looks really good
I put my wings in the baking pan on a cookie sheet to keep the drippings from making the wings soggy on the pan side. All in all looks delicious.
If you take the rooks movement, and reduce each longer move to a series of single steps a1a2a3a4 for example, this becomes a Hamiltonian problem. The corners have 2 nodes, the edges three, and the core has four. Black and white indicates even or uneven distance in nodes.