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 re(2): And some more by Erik O.)

Thanks for answering Erik, this means that we either have to do a search for 18 digit (followed by 00) numbers or 20 digit numbers or something completely different like building perfect squares that will stay perfect squares when adding a number in front of/behind of it.
I did an extensive Google search for 18/20 perfect squares, buth only (useless) palindromic turned up.

6 digit perfect squres are (To my humble opinion) useless.

Posted by Hugo on 2005-03-29 19:49:12