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: And some more by Hugo)

Hugo,

I don't have a best solution, yet.

The source where I got this little puzzle indicated that there is at least one number which scores over 100.  That number was not listed in the source.

I'll try to write a little program over the weekend to see if I can come up with a single best number.  It shouldn't be to terribly difficult to write, and there's only 20! permutations to run through (only 2.4329 x 10^18).  ;)

Posted by Erik O. on 2005-03-29 17:47:53