Substitute each of the capital letters by a different digit from 0 to 9, such that each of the columns, each of the rows and each of the two main diagonals of this 5x5 grid have the common sum 275. None of the numbers in the 25 cells contains a leading zero.

RL   AA   CN   BD    RC
AE   MC  ML   EA    RB
UA  MB   EE   LR    AU
BR   EU   LM   LN    UE
BN   LD   NC   UU   BM

I began firstly with the following grid on the realisation that what was required would have its foundation here:

17  24   1    8  15
23   5    7  14  16
  4   6  13  20  22
10  12  19  21   3
11  18  25   2    9

This has the "magic" constant 65.
If one multiplies each cell by 3 and adds 16 the "magic" constant becomes 275.

It is then just a matter to assign digit values to the letters:


A B C D E L M N R U
 8 4  1 0  5 7  3  9  6 2

The grid:
67  88  19  40  61
85  31  37  58  64
28  34  55  76  82
46  52  73  79  25
49  70  91  22  43

Posted by brianjn on 2009-10-11 21:04:31