See the boxes and the numbers given below:

                        +---+---+---+---+                          
                        |   |   |   |   |    1937 3684 1981 4759 6491
+---+---+---+---+       +---+---+---+---+    5753 9108 0784 6737 1645
|   |   |   |   |       |   |       |   |    0093 4628 5998 4748 2896 
+---+---+---+---+---+---+---+       +---+    1388 4769 3266 1919 1499
    |   |   |   |   |   |   |       |   |    7572 9598 2376 5879 7891 
    +---+   +---+---+---+---+---+---+---+    2648 8472 1763 8473 1618 
    |   |   |   |       |   |   |   |   |    4784 1683 9184 8176 2637
    +---+---+---+---+   +---+---+---+---+    0134 2773 1839 3711 3674 
    |   |   |   |   |       |   |            4782 1687 4573 1679 4723 
    +---+---+---+---+       +---+            4623 5743 2648 1894 1679
                |   |       |   |            4897 4734 9914 7598 7238
                +---+---+---+---+            1734 4789 3716 1562 1847 
                |   |   |   |   |
                +---+---+---+---+
                |   |
                +---+

Fill in the boxes with 12 numbers chosen from the list, one digit per box. The given numbers can be written from left to right, right to left, up, or down. And you canīt use a number more than once (unless it's listed twice). When all the boxes are filled, sum up all digits in the boxes (not the numbers that you used). This is YOUR score.

Whatīs the maximum score YOU can achieve?

Note: this meant to be a contest among users so, to make it fair, avoid using a computer. We are not asking for the maximum score that can be obtained, we are asking for the maximum score that YOU can achieve. And you may post YOUR SCORE in the subject of your comment. The winner (after a reasonable time) will gain an apple (the fruit, not Steve Jobsī).

I came up with a 230 solution (which I will show if necessary but it's not as good as Satan's two 239's--well done!).

The rank ordering of number sums is useful for identifying which numbers carry the most overall weight.  A similar rank ordering of the number products (e.g., 9574 would be 9X5X7X4 = 1,260)give a slightly different order but may also be useful in deciding which numbers to try in the matrix.  Additionally, maximizing the over total means maximizing the numbers that are not at intersections, and placing the smaller numbers at the intersections.  See Satan's solutions and you'll see that even though he has a 1 and 2 in his solution, they are at intersections so they don't detract from the overall sum as much as they would if they were at non-intersections.  The smallest number he has at a non-intersection is a 5.  I'm still looking for an improvement on his solution using the ideas above.

Posted by dopey915 on 2005-11-01 16:05:00