Alice loves magic squares. She has a 4x4 square, where she can put a number in each cell. But alas! Some evil person has poked a hole in her square. Alice is really really sad because she can't make a magic square anymore. Won't you cheer poor Alice up?

You are given a 4x4 square with 1 of its cells removed. Put the numbers 1 to 15 in it so that each row, column and diagonal sum to the same.


1 Answer 1


Here are a few from this site. Any magic square with integers 0-15 will work, considering the 0 as a hole. I've chosen four with the 0 in the inner four cells just to be sure it meets your criteria. The rows, columns, and diagonals of each add up to 30.

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    $\begingroup$ The square can be constructed by making a normal 4x4 1-16 square and subtracting 1 from each cell. $\endgroup$
    – jingyu9575
    Commented Sep 16, 2015 at 3:53
  • $\begingroup$ Actually it can be done even if the hole (ie. 0) is in a corner or a side as well. $\endgroup$
    – Rohcana
    Commented Sep 16, 2015 at 5:02
  • $\begingroup$ Building on @jingyu9575 his suggestion, you can extend the idea behind it up to (and maybe beyond) a 16x16 (puzzling.stackexchange.com/questions/6250/…) , just reduce each of the numbers by one. $\endgroup$ Commented Sep 16, 2015 at 8:40

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