Papy wrote:For your crasy grid I regard.

It seems that the problem is in sample sudoku

It must use a bad recursive method(PERHAPS)

it was your crazy grids from a previous post

I said it had many solutions because I feared it might be counting the number of atoms in my cpu chip

if a program goes haywire the top three things to check are

(1) the input

(2) the program

(3) the task

in this case neither the input nor the program is bad

in this case the task is unreasonable with respect to human lifespan

the program will just take a long time to count many solutions

now, knowing this, the programmer may look at the problem differently

if the count is all that's necessary then each solution need not be generated to be counted

(the two programs cited count solutions by solving, but that's ok, they are tasked to solve)

this observation is where isomorphism and permutation groups stepped in and made it possible

to count all completed sudoku grids without generating each and every one

papy, you seem to be hooked on using counting to detect puzzle differences

I gave a hint that looking at candidate grids may be a good place to start

this will work sometimes, but not in all cases

(this means: don't use counting to prove isomorphism)

for these two puzzles (posted by you from gordon's 17's)

- Code: Select all
`.......81.3.2..............1.8.6..4....7..3..6........5..3..7...9....2......1....`

.......81.3.2..............1.8.6..4....9..3..6........5..3..7...7....2......1....

the number of pencilmark grid cells with i candidates (not counting clues), 1<=i<=9 is

- Code: Select all
`0.2.4.20.21.10.6.1.0`

0.2.4.18.21.12.6.1.0

and the number of pencilmark grid cells with candidate i is

- Code: Select all
`17.32.18.49.49.36.32.31.47`

17.32.18.49.49.36.35.31.48

in the second case, if 7 and 9 were interchangeable up to isomorphism,

the 7th and 9th entries above would also have to be interchanged