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Sums of squares and stuff. (Posted on 2005-03-26) Difficulty: 3 of 5

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?

See The Solution Submitted by Erik O.    
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Comments: ( Back to comment list | You must be logged in to post comments.)
a few more | Comment 3 of 16 |
This one has 45 points:

86497225009548131367

Pts  Square
4     8649     93^2
2     64         8^2
2     49         7^2
4     7225     85^2
6     722500  850^2
3     225       15^2
5     22500   150^2
2     25         5^2
4     2500     50^2
5     95481   309^2
2     81        9^2
4     3136     56^2
2     36         6^2
  Posted by Larry on 2005-03-27 13:51:27
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