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King Walking




Starting on any square of the grid the king can make successive moves to any of its 8 neighbors or itself. The king constructs numbers by collecting the digits of every square that he visits during his walk, including the starting digit. In the example at left, if the king starts in the top-left corner then he will be able to collect the following numbers: 2, 22, 27, 28, 29, 222, 270, 283 and many others. However no matter where he starts, the king will not be able to construct 45. Submit an NxN grid of digits, such that the smallest number that cannot be made is maximal. This puzzle is divided into 10 parts where N is from 4 to 13, inclusive.


Scoring:  Your raw score for each part is the smallest positive integer that can't be made. Your subscore is your raw score divided by the contest best raw score, cubed and then multiplied by 10.0000. For example, if your raw score is 45 for N(4) and the best of contest raw score is 59, then your subscore is ( (45 / 59) ^3 ) * 10.0000 = 4.4369, where the the remaining decimals are truncated. The subscores for all 10 parts are added together to compute your total score, with 100.0000 being the best possible score.

Submissions:  Submissions must contain N^2 digits ranging from 0 to 9 in row major order. All other characters, such as white space and punctuation are permitted and will simply be ignored by the scorer. Example: For the grid above, one way to submit the grid is 2937,7815,6029,1436.