A     B     C     D     E
   +-----+-----+-----+-----+-----+
   |     |     |     |     |     | 
   |  1  |  7  | 13  | 20  |  6  |
   +-----+-----+-----+-----+-----+
   |     |     |     |     |     | 
   | 25  |  9  |  2  | 23  | 11  |
   +-----+-----+-----+-----+-----+
   |     |     |     |     |     |     
   | 14  | 22  | 17  |  8  | 16  |    
   +-----+-----+-----+-----+-----+
   |     |     |     |     |     |      
   |  4  | 12  | 10  |  3  | 19  |    
   +-----+-----+-----+-----+-----+
   |     |     |     |     |     |      
   | 24  | 18  |  5  | 15  | 21  |  
   +-----+-----+-----+-----+-----+

Add together five different numbers from the grid above to achieve the highest possible total. Starting at column A and working your way across to column E, only one number may be chosen from each column, and no two numbers may be from the same row or diagonal line.

I found all possibilities using 25 or 24 from column A.
The highest sum is 25+18+17+20+19 = 99

This is clearly higher than can be achieved by starting with 1 or 4.
It is also higher than can be achieved by starting with 14, since this rules out using 25, 24 and 22.

Incidentally if you want the lowest total and you start with 1 you get 1+12+5+8+11=37.  This is not as near the sum 1+2+3+4+5 as the highest sum is to 21+22+23+24+25 so my guess is this chart was made with the high sum 99 in mind.

Posted by Jer on 2013-05-21 15:41:58