Melody

It is good to see that our answers are getting looked at   

Thanks Rom and guest.

thanks 

ok, thanks 

Thanks,

It doesn't really matter, I was trying to work out how to get them without a computer program.

Can you print them in groups so that the ones with the same digits are together?

Do you know if you got 13 combinations of 6 digits?

I know 0123467 is not divisable by 23.

Its digits do however add to a 23.  Maybe if those digits are rearranged then you will get a number that IS divisable by 23.

I have found 13 sets of 6 numbers.  Each set comply with the first and 3rd conditions.

0123467 is one of those sets.

Now it is a matter or rearranging the digits  in each set to work out which permutations of digits will give a number divisable by 23.

I have just been playing with the numbers. I do not know how to do this.

But these are the possible combinations of 6 digits that add up to 23.

0 1 2 3 8 9

0 1 2 4 7 9

0 1 2 5 6 9 

0 1 3 4 6 9 

0 2 3 4 5 9

0 1 2 5 7 8

0 1 3 4 7 8

0 1 3 5 6 8

0 2 3 4 6 8

1 2 3 4 5 8

1 2 3 4 6 7     (added on)

0 2 3 5 6 7 

0 1 4 5 6 7 

So that is 12 groups of 6 digits.

Now it canot begin with 0 becasue that would not be a proper number.

The digits add to 23 so none of these will be divisable by 3 or 6 or 9.  I am not sure what that means, I am getting in a mess.

So I have a lot  LESS than

5*5!*11+6! =6600+720 = 7320 ways   

plus another  720 =  8050 

352 ways certainly sounds possible

Edit

oh dear, I just realize that 1 2 3 4 6 7 is missing.    I wonder how many others are missing.  I think not many, hopefully none.

It cannot equal 0.

It must be bigger than 0

Any more takes?

ok, still I think when there is possible confusion (over and above knowing the very basic rules) people should just use brackets.

That indice one gets me every time!

How did you get 165?

Yes I think i like that one better.  that makes good sense I think....