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We can say that an $n$-by-$n$ square is regular provided that:

  1. Each of the integers from $0$ to $n^2 − 1$ appears in exactly one cell, and each cell contains only one integer (so that the square is filled), and

  2. If we express the entries in base-$n$ form, each base-$n$ digit occurs exactly once in the units’ position, and exactly once in the $n$’s position.

What is an example of a 4-by-4 filled, magic square which is not regular? The square should use the integers 0 to 15. Show the answer in both decimal and base-4 as well.

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    $\begingroup$ I don't know what you mean by a irregular magic square? :P (I'm guessing its a stupid question, sorry :P ) $\endgroup$ – The Dragonista Feb 20 '15 at 20:42
  • $\begingroup$ @TheDragonista In my last question I defined what a regular square is. $\endgroup$ – Daniella Feb 20 '15 at 20:44
  • $\begingroup$ My previous one was irregular, so shall i post that answer here and try finding a different solution for the other one? $\endgroup$ – The Dragonista Feb 20 '15 at 20:52
  • $\begingroup$ I think Togashi already did $\endgroup$ – Daniella Feb 20 '15 at 20:54
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    $\begingroup$ Would it be possible for you to include in this question what you mean by a regular square? I'm pretty sure this isn't a term that most people know with regards to magic squares, and questions need to stand alone. Thank you! $\endgroup$ – Aza Feb 20 '15 at 21:00
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Finally!! I've got it! :) :D

Answer

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