Arrange two of each digit (0-9) into a 20 digit long number, which does not begin with a zero, then score your number as follows:

For every 2 digit sequence that forms a perfect square score 2 points, for every 3 digit sequence that forms a perfect square score 3 points. A four digit square would score 4 points, and so on.

For example, if your number was 58738219024971503664, then you would score 2 points each for 49, 36, and 64 and 6 points for 219024 giving a total of 12 points. You may not count 036 as a three digit square.

What is the maximum number of points you can score?

The two following numbers may be the start for a further computer based search, by looking at permutations of the numbers (not used in the 13 digit square) in front of the 13 digit square.

347 6889 3941217562500
Where 6889 scores 4 points and
25         .                 2
2500                       4
625                         3
62500                     5
5625                       4
562500                   6
75625                     5
7562500                 7
2175625                 7
217562500              9
39412175625         11
3941217562500     13 for a total of 80 points

6788 141 39312975625 would score 79 points

Posted by Hugo on 2005-03-31 12:42:34