by dukuso » Thu Jul 21, 2005 1:59 pm
Hi Colin,
again I have problems to understand you.
Probably you are referring to earlier messages, but I don't want
to look them up now. (I didn't understand parts of them either...)
>There might even be two equivalent ways of expressing the solution !
what you mean ? Which solution ? How "express" ?
>From:
>The number of ways to fill a shute is 9!* 56*216^2 and
chute, not shute
>Red Ed has published the frequency n of these as the gang of 44
>9!* 56*216^2= the sum of k*[n1+n2+n3...........n43+n44]
sum over k ?
>1. N= the sum of [44^2] of the possible 44*k*n*each of the
> possible 44*k*n * B5*B9 solutions
what's N ?
sum of [44^2] over which summing-index ?
>or
>
>2. N= 9!*[56*216^2]^2 * the sum of each of the 44^2 - B5*B9 solutions.
N is the total number of sudoku-grids ~6.67e21 ?
9!*[56*216^2]^2 is the number of way to fill B1,B2,B3,B4,B7 ?
sum [i,j=1..44] X(i)*X(j) is the number of ways to B5,B9 ?
This depends on B2,B3,B4,B7 of course.
And, it's not an invariant of the 44gang-type.
>From Red Ed we know that The Box 2 is one of 8 different combinations
>[frequencies of 25,8,4,4,1,1,1&1] and we know that Box 3 can have
>around 33 conbinations.
..provided what ? combinations of what ?
>That makes around 8^2 possible combinations
>of B4/B2
..given B1 ?
> and 33^2 possible combinations of B7/B3
given B1,B2 resp. B1,B4 ?
>One would have to analyse each of the 56*216-B2s and the 216-B3s to
>determine their frequecys of the actual pairings.
...to achieve what ? You are looking for another way to compute
the total number of sudoku-grids ? (~6.67e21)
>[May be this is
>is the gang of 44 !]
>
>[I find the working out of the possible solutions of 6 clue
> completion of B5 given B2/B4 quite taxing - but it must be
>relativly easy to programmers]
when the numbers are not so big, you can just backtrack
through the whole sub-problem-space.
If you want to calculate the 6.67e21 by splitting into
B1+B2+B3+B4+B7 and B5+B6+B8+B9 , then yes, I think it
can be done. But we already have enough confirmation
of that number, so it's not so important
Guenter.