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?

(In reply to And some more by Hugo)

64 points with 361874529 361874529 00

points square
11      36187452900     190230^2
9        361874529        19023^2
9        361874529        19023^2
7        7452900            2730^2
5        74529               273^2  
5        74529               273^2
5        52900               230^2
3        529                  23^2
3        529                  23^2
3        900                  30^2
2        36                    6^2
2        36                    6^2

Erik O, could you confirm that you are absolute sure that your solution is the best possible.  If you aren't sure, could you post a target we can beat?

Posted by Hugo on 2005-03-28 17:32:32