champagne wrote: I found only 75 puzzles having the exocet pattern in the rand 8.6 file
Taking these data as they are:
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Distribution of clues in the 75 list with exocet:
nb-clues nb-instances
19 0
20 0
21 0
22 3
23 14
24 19
25 24
26 12
27 2
28 0
29 1
30 0
31 0
32 0
33 0
34 0
35 0
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Distribution of clues in the full list of 282588 puzzles
nb-clues nb-instances
19 0
20 2
21 283
22 5814
23 36563
24 87547
25 91557
26 46586
27 12283
28 1794
29 149
30 10
31 0
32 0
33 0
34 0
35 0
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Proportion of puzzles having an exocet:
nb-clues proportion
19 0
20 0
21 0
22 3/5814
23 14/36563
24 19/87547
25 24/91557
26 12/46586
27 2/12283
28 0
29 1/149
30 0
31 0
32 0
33 0
34 0
35 0
Results recalled from here: http://forum.enjoysudoku.com/the-real-distribution-of-minimal-puzzles-t30127-8.html
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Weights:
#clues %puzzles
20 0.0
21 0.000034
22 0.0034
23 0.149
24 2.28
25 13.42
26 31.94
27 32.74
28 15.48
29 3.56
30 0.41
31 0.022
Application of the formula in the above-mentioned post
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Unbiased proportion of puzzles having an exocet
nb-clues weighted-proportion * 100
22 3/5814 * 0.0034 = 1.75438596491228e-06
23 14/36563 * 0.149 = 5.70522112518119e-05
24 19/87547 * 2.28 = 0.000494819925297269
25 24/91557 * 13.42 = 0.00351780857826272
26 12/46586 * 31.94 = 0.00822736444425364
27 2/12283 * 32.74 = 0.00533094520882521
28 0 = 0
29 1/149 * 0.022 = 0.000147651006711409
Estimated unbiased proportion of puzzles having an exocet in the SER > 8.6 area
(+ 1.75438596491228e-06 5.70522112518119e-05 0.000494819925297269 0.00351780857826272 0.00822736444425364 0.00533094520882521 0.000147651006711409)
= 0.017777395760567%
= 0.018%
This is a small proportion (less than 2 in 10,000), although this is more than I expected. The reason is, there are more cases than expected with more than 24 clues.