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Puzzling

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  • $\begingroup$ I will ask a second question for other dimensions however until then thank you for the answer. $\endgroup$ Commented Nov 22, 2017 at 17:23
  • $\begingroup$ So problem with solving (4,3,2,1) is because N is even? Because I tried solving it and got nowhere. $\endgroup$ Commented Nov 22, 2017 at 17:40
  • $\begingroup$ Sorry I mean't (4,3,1,2) not (4,3,2,1) $\endgroup$ Commented Nov 22, 2017 at 19:02
  • $\begingroup$ Yes, (4,3;1,2) is not solvable because the top-left and bottom-right are always even, and the other two always odd. This is because here all four tiles are of the same type (if the checker board colouring you choose has the top-left square white, then they are all e-tiles). $\endgroup$ Commented Nov 22, 2017 at 21:04
  • $\begingroup$ Thanks a lot for the detailed answer I really appreciate it. My proof (if you can call it that) was that algebraically the proportions aren't the same as those that can be solved. But I can't prove this for all the infinite proportions so thank you for your solution. $\endgroup$ Commented Nov 22, 2017 at 22:27