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 I wonder if 67 can be topped... by Jer)

36187452936187452900

361874529 both for 9*2
36187452900 for   11
36 both for             2*2
361 both for           3*2
529 both for           3*2
52900 for               5
74529 both for        5*2
7452900 for            7
900 for                   3

gives 70

And Jer, go get your own number ;)

Posted by Hugo on 2005-03-28 19:03:26