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.