The integers 1 to 50 are placed around a circle in such a way that the sum of any two of them which are adjacent is a perfect square. Of these integers, all but the prime integers were removed. Restore the missing integers.enter image description here.


1 Answer 1


Here's what I believe to be the (unique) solution:

enter image description here

  • $\begingroup$ From Where did you get the circle $\endgroup$
    – rudra
    Commented Nov 29, 2017 at 2:39
  • $\begingroup$ Isn't it obvious? The circle is the one used by the OP. $\endgroup$ Commented Nov 29, 2017 at 3:18
  • $\begingroup$ Any good approach for the answer? $\endgroup$
    – geeky me
    Commented Nov 29, 2017 at 16:19
  • $\begingroup$ There's nothing very fancy. To fill in a single-space gap you can look for things that produce squares when added to both (known) neighbours, and in the cases here there was only one possibility. For a two-space gap you look for possible neighbours of the two known cells on either side, and then see which pairs add up to make a square. For longer gaps you need (or at least I needed) to draw a graph (in the vertices-and-edges sense) showing what can be next to what, and then look for paths through it. $\endgroup$
    – Gareth McCaughan
    Commented Nov 29, 2017 at 16:21

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