Look at the grid below :

          +------+------+------+------+------+
    1 ==>           +5            +4         |
          +      +------+      +------+      +
          |  +2  |      |  +1  |      |  x2  |
          +      +------+      +------+      +
          |         -1            +8         |
          +      +------+      +------+      +
          |  +1            x2            +5  |
          +      +------+      +------+      +
          |         +5            +5        ==> X
          +------+------+------+------+------+

Entering the grid by the upper left corner with 1, you can trace a continuous path following through the +5 (obtaining 1 + 5 = 6), then through the +1 (obtaining 6 + 1 = 7), then through the x2 (obtaining 7 x 2 = 14), then through the +1 (obtaining 14 + 1 = 15), then through the +5 (obtaining 15 + 5 = 20), then finally through the +5 (obtaining 20 + 5 = 25), exiting the grid, and your (small) score is X = 25. Certainly you can achieve a greater score following through the grid by another path. The unique restrictions are that you canīt pass through the same way more than once and that the path must be continuous. More, you are not obligated to pass through all the grid and you can cross your path along the way. In fact, in this sample grid you can achieve X = 61.

Given the grid below (where the rows and columns are identified to make clear your path), whatīs the greatest score that you can achieve?)

         (A)    (B)    (C)    (D)    (E)    (F)    (G)    (H)    (I)    (J)    (K)    (L)    (M)
      +------+------+------+------+------+------+------+------+------+------+------+------+------+
 1 ==>          +3            +5            +1            +3            -1            +4         |    
      +      +------+      +------+      +------+      +------+      +------+      +------+      +
 (2)  |  +2  |      |  +7  |      |  +3  |      |  +4  |      |  +8  |      |  +1  |      |  x2  |  
      +      +------+      +------+      +------+      +------+      +------+      +------+      +
 (3)  |         +5            -2            +8            -1            +2            +2         |  
      +      +------+      +------+      +------+      +------+      +------+      +------+      +
 (4)  |  -1  |      |  +3  |      |  +9  |      |  +2  |      |  x2  |      |  +4  |      |  +1  |  
      +      +------+      +------+      +------+      +------+      +------+      +------+      +
 (5)  |         +7            -1            +3            -1            +3            +8         |  
      +      +------+      +------+      +------+      +------+      +------+      +------+      +
 (6)  |  x2  |      |  +5  |      |  +5  |      |  +4  |      |  +5  |      |  +2  |      |  +6  |  
      +      +------+      +------+      +------+      +------+      +------+      +------+      +
 (7)  |         +2            +8            +2            +8            +4            +4         |  
      +      +------+      +------+      +------+      +------+      +------+      +------+      +
 (8)  |  +1  |      |  -1  |      |  +1  |      |  x3  |      |  +2  |      |  x2  |      |  +1  |  
      +      +------+      +------+      +------+      +------+      +------+      +------+      +
 (9)  |         +2            +5            -1            +7            -1            +5          ===> X
      +------+------+------+------+------+------+------+------+------+------+------+------+------+

Note: We are not asking for the "MAXIMUM" score that can be achieved. We are asking for YOUR score. Also, to make this fair, for those who will use the computer, I ask gently to not post the score obtained this way.

Unless I added wrong, If one could fly this puzzle and scoop up the numbers in the best possible order regardless of path, I come up with 8544=1+177 (all additions) * 48 (all * 2,2,2,2,3).  So that being the case getting where others have gotten is pretty good.  I would like to see the computer total (without the path initially) to see if we can match it.  Perhaps put the score in the subject and the path in the comment.  Gently asked.

Posted by john on 2005-08-04 15:45:15