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.
.
$\begingroup$
$\endgroup$
asked Nov 28, 2017 at 23:20
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
4
Here's what I believe to be the (unique) solution:
answered Nov 29, 2017 at 2:27
-
-
$\begingroup$ 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 meCommented 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