tarek wrote:I'm not sure who is keeping track of all posted singles M3 puzzles. They used to be quite rare in 2007 before their numbers exploded!!!

Not me.

tarek wrote:What comes next is to see what singles M3 puzzle has the least number of backdoor triplets. Could there be a puzzle with only 1 singles backdoor triplet? A search in the neighbourhood of that puzzle might bring some unexpected results

gsf wrote:ronk wrote:What do the last two numbers (the '60' and '109') below mean?

- Code: Select all
`..1.....2.5...3.4.6.....7......2.....8.9.6.3....5.8.....2...1...3.4...5.7.......6 # 74201 FNBP C21.m/M2.60.109`

Do the meanings change for -q1, -q2, and neither of these two?

the last tuple is M(M).(M1).(M2)

you can see the descriptions for M,M1,M2 under EXPRESSIONS

M: (backdoor) The backdoor (magic cell set) size

M1: (magic) The number of backdoors (magic cell sets).

M2: (guesstimate) The estimated number of guesses before a backdoor hit.

So "mm" or (M1) is the number of backdoor triplets in question. Thank you, ronk.

Two questions arose

1) Could

the order of selection of the backdoor cells affect the backdoor size or the number of triplets?

2) Are there additional rules in estimation of "nn" such as "try bivalues first" or it is assumed that some cell is blindly guessed to some value within its pencilmarks?

The answer to the first question is likely to be "no" but I am prepared for any surprises from sudoku.

Regardless the existence or non-existence of additional rules/constrains involved in "nn" calculation, this property looks fragile.