In the traditional 3 x 3 Magic Square the digital sum ("magic" constant) is 15. The square may be duplicated such that each cell has two identical digits forming a
T U combination (eg 11,22) with the common value being 165 .

The digits 1 to 9 may be placed in each cell so that each Tens digit and each Units digit is represented once in the 3 x 3 grid with no digit reappearing in the same column or row; the column and row totals are to have the same value.

While I can offer a solution with all sums but one major diagonal having the same "magic" constant, can you do similar, or even better, offer 8 equal digital sums?

(In reply to computer solution by Charlie)

Charlie,

Personally I hate computer solving when logic can get you there, that really is the object of most presenters.

In this case it is blatantly clear that it would take forever to meet my transaction without what technolgies can provide.

I have edited your list for the most row and diagonal matches for "165" mainly because I didn't initially understand your focus; these being they:

 165  162  165
 165  168  165
 165  165  246
 165  165  174  *
 165  165  255
 165  192  165
 165  195  165


I note that my solution is at #4 which clearly is not as good as the top of the list.

Posted by brianjn on 2009-10-17 02:06:17