(In reply to
re: solution by Federico Kereki)
What I was saying was that the individual cycles could not be greater than 7, not that the resulting interplay, or beating, or combination of the cycles cannot exceed 7. Indeed, one of my cases had a 2cycle and a 5cycle for a total cycle length of 10. What you can't have is, say, a 5cycle and a 13cycle, as a 13cycle can't exist with only 7 items to permute. And a 10cycle can only exist as a 2cycle and a 5cycle, not as a case where a goes to b, b goes to c, c goes to d, ... , i goes to j, j goes to a, because h, i and j do not exist within the set being permuted.
The cycle lengths making up the complete cycle have to add up to seven (counting the 1cycles which stay the same), and they're all positive, so none can be larger than 7.
The total cycle length of 12 does not work in the case presented as 2080 is not divisible by 12, which, further, is the case as 2080 is not divisible by 3.
I believe I presented all cycles that are made up of subcycles not exceeding 7. Only one of those overall cycles exceeds 7the one made up of 2 and 5. But it's irrelevant whether the compound cycle exceeds 7 or not.

Posted by Charlie
on 20070818 01:14:24 