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High Scorer (Posted on 2013-05-21) Difficulty: 3 of 5
    
      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.

No Solution Yet Submitted by K Sengupta    
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Solution Solution | Comment 1 of 11
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
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