Back in An Arrangement of 15 you were asked to place the numbers 1 to 15 in a line so that any two adjacent numbers summed to a square number.

Now, try to arrange the numbers from 1 to 32 in a circle, so any two adjacent numbers again sum a square number.

If you've got ms excel then you can do this by using the drawing features of excel.

First, you need to list the 46 possible ordered pairs of numbers that add up to the squares.  Each of these represents a line connecting vertices that are number 1 to 32.  Create this graph in excel using the boxes or circles and then using the conectors.  The nice feature is that you can move the vertices around by dragging and dropping, and the lines move with them, maintaining the overall integrity.  The observations noted by others here can be quickly implemented.  The solution emerges quickly.

Posted by bernie on 2005-01-10 13:19:01