.

coloin asked me how many grids might prove to have 9B + 8 puzzles,and just how many there might be among all CF grids (53M).

I tested small batches of CF grids, with the following results.

- Code: Select all

nsUA Sample NG17P TN17P Avg Max

--------------------------------------------

11 first 20 19 564 28 184

last 20 20 5481 274 3429

25 first 20 12 355 12 60

last 20 13 928 45 370

40 first 20 8 16 1 4

last 20 5 31 2 21

Non-pool?

random 50 0

- nsUA is the number of small UA's (size <= 12), which corresponds to my division of the 10C/11C candidate pool as described above. For each sample I tested the first 20 grids inn the list, and the last 20, bearing in mind that each grid list is in CF order. For the last sample I drew 50 grids at random from the rest of the grids.

- NG17P is the number of grids for which a 9B + 8 puzzle was found, TN17P the total number found

- there is a strong correlation between nsUA and existence of 9B + 8 puzzles

- there is a bias towards grids with high index numbers, a bias which persists across all the 11C search functions I've run (note also that 50% of the known 11C grids are clustered at the high end)

Based on this admittedly small, but revealing, sample, I'd say that 99% - 100% of grids with 9B + 8 puzzles are to be found in our 611,502 grid pool.

Pool grids have high probability of having 9B + 8 puzzles, maybe 30-40% of them. If the average number of 9B + 8 puzzles per grid is around 20-30, then the total number might be as high as 1M to 2M.

Sadly I neglected to report the actual number of 9B + 8 puzzles in the

Find11C program which is currently running, and which generates 9B + 8 puzzles as part of the process. I've rectified that now, and all searching from here on will log these details, so we can get some idea of what the real numbers are, and how good my estimates are, as the search progresses.

Speaking of which, we've searched 18% of the pool, and still no cigar!