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?

139348164782975625 00

25   
625
5625
75625
2975625
64782975625
2500   
62500
562500
7562500
297562500
6478297562500
81
3481
16

scores 84.
A program would be necessary to test if permutations of the 7 leftmost digits could be combined with the 13 digit number to form a 19 or 20 digit square.  Up to 17 digit my program didnt round the square and with a little trick I could do 18 digits also.

But 19 and 20 digits are above the precision of what I have on my computer. 

 

Posted by Hugo on 2005-04-01 14:53:04