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Double the Magic (Posted on 2009-10-16) Difficulty: 3 of 5
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?

  Submitted by brianjn    
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Solution: (Hide)
     82  14  69   165

     36  58  71   165

     47  93  25   165

174 165 165 165   165
Charlie posted a list of possible scenarios.

Of those I edited values compliant with my criteria which follow:

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

My offered solution is at #4 which clearly is not as good as the top of the list that one being:

     21   98   46  165
         
     79   54   32  165
        
     65   13   87  165

165 165  165  165  162

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: computer solution - missed me, no!brianjn2009-10-17 02:06:17
Solutioncomputer solutionCharlie2009-10-16 18:59:07
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