*[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!

## New Rules

(*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….

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## Have more fun on *Let’s Play Math!* blog:

- 2010 Mathematics Game
- 2009 Mathematics Game
- 2008 Mathematics Game
- 2007 Mathematics Game
- Puzzles for the New Year