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.