Number of combinations of a six digit number (with a twist).

Factual Questions
1

What is the formula for finding the total available combinations of a six digit number with the following criteria;

  1. You have to use all six digits.
  2. You can’t use any zeros.
  3. You can’t have the same two numbers show up in the six digit string together.

I get the first two. It would be 99999*9=531441, but that would include repeats of numbers. Now solve for the third criteria.

2

Your solution uses all nine numbers each time, but the amount of avaiable numbers goes down as you use 'em. So the answer is 98765*4=60480. I think.

SD

3

Not quite sure what that means. You can’t have the same number next to each other? So 121212 is OK but 121211 is not? If so, I think the answer is 98888*8. The first digit can be anything; each successive digit can be anything other than the preceding digit.

If you mean each number can be used only once, then it’s 98765*4.

4

9 X 8 X 7 X 6 X 5 X 4 = 60480

5

Er, I get 10[sup]6[/sup]=1,000,000 for (1), if by the criterion in (2) you are suggesting that all ten digits 0-9 are available for (1).

Or am I misunderstanding the problem?

And I believe that Spacedog is correct for (3).

6

No zeros, so you’d only have 9 numbers.