[Photo by pfala.]
Thanks to John Cook’s article about factorials in the recent Mathematics and Multimedia Carnival, we’re adding new rules to the 2010 Mathematics Game.
Let’s play with multifactorials!
(n!)! = a factorial of a factorial
n!! = a double factorial = the product of all integers from 1 to n that have the same parity (odd or even) as n
n!!! = a triple factorial = the product of all integers from 1 to n that are equal to n mod 3
= product of all integers from 1 to n that are equal to n mod k, where both n and k must be constructed from the year digits
I did a search this morning and realized that John’s article barely scratched the surface of the topic. I think we need to draw a line somewhere. So we will allow multifactorials (with the above limitation regarding n and k) but not subfactorials, superfactorials, hyperfactorials, alternating factorials, primorials, etc.
This week is hyper-busy, so I won’t have time to explore these new numbers for several days. But I look forward to hearing what you all come up with….