Digits Number of puzzles
1 31,200 with unique solutions
37,102 with no solutions
406,250 with 4..32 solutions
474,551 total puzzles
2 10,795,200 with unique solutions
1,990,652,352 with no solutions
6,339,278,400 with 3..476 solutions
8,340,725,952 total puzzles
3 33,433,717,226 with unique solutions
6,746,392,175,276 with no solutions
139,816,773,439,850 with 2..1200 solutions
146,596,599,332,352 total puzzles
4 1,974,825,396,897,600 with unique solutions
240,014,957,704,387,2?? with no solutions
1,147,855,057,502,310,0?? with 2..3840 solutions
1,389,844,840,603,594,8?? total puzzles
2,576,581,829,865,418,742 total random letter choices
1,186,736,989,261,824,0?? with over 10 different letters
Digs Uniq None Dupl Max
1 6.57% 7.82% 85.61% 32
2 0.13% 23.87% 76.00% 476
3 0.02% 4.60% 95.38% 1200
4 0.14% 17.27% 82.59% 3840
And I suspect the odds just get worse after this. (And note that the numbers have gotten too complicated for both Perl and me toward the end there so don't use these for lifeanddeath calculations.)
