After the heavenly race, each sign went back to a month of the year, but without caring whether it was "its" month, or if there already were other signs in that month.

In how many ways can the signs be assigned to months in this way? Isn't this the same answer as in that problem? Why/why not?

As each sign has a choice of 12 months to go to there are 12^12=8,916,100,448,256 ways of assigning the signs to the months.

This is different from Horoscope Hijinks I, as in this later puzzle, empty months count as a difference. For example if the first 6 signs all congregate in month 1, and the last 6 signs congregate in month 5, that's different from those same identical groups  congregating in months 2 and 8, etc.  For this same C(12,2)=66 ways, the former puzzle had only one way: first 6 signs tied for positions 1-6 and last 6 signs tied for 7-12.

Posted by Charlie on 2006-12-05 14:26:51