8Dec/083

## MMM #21: How many divisors?

Blinkdagger has announced the winner for MMM #20. Congratulations, Diego Vila Cid!

Now, onto MMM #21.

I have a Rubik’s Revolution, courtesy of Techno Source (or $10 Amazon.com gift certificate, if you prefer, or $10 in USD via PayPal to non-US folks) to give to the winner.

Here's the problem:

10 is said to have 4 divisors because 4 whole positive integers (1, 2, 5, and 10) divide it. How many divisors does 10! have, where 10! = 1x2x3...x8x9x10? Show how you calculate your answer.While you might write a computer program to verify your answer by brute force, computer solutions are not accepted.

Here are the rules for the contest:

- Email your answers with solutions to mondaymathmadness at gmail dot com.
- Only one entry per person.
- Each person may only win one prize per 12 month period. But, do submit your solutions even if you are not eligible.
- Your answer must be explained. You must show your work! Wild About Math! and Blinkdagger will be the final judges on whether an answer was properly explained or not.
- The deadline to submit answers is Tuesday, December 16, 12:01AM, Pacific Time. (That’s Tuesday morning, not Tuesday night.) Do a Google search for “time California” to know what the current Pacific Time is.)
- The winner will be chosen randomly from all timely well-explained and correct submissions, using a random number generator.
- The winner will be announced Friday, December 19, 2008.
- The winner (or winners) will receive a Rubik’s Revolution or a $10 gift certificate to Amazon.com or $10 USD via PayPal. For those of you who don’t want a prize I’ll donate $10 to your favorite charity.
- Comments for this post should only be used to clarify the problem. Please do not discuss ANY potential solutions.
- I may post names and website/blog links for people submitting timely correct well-explained solutions. I’m more likely to post your name if your solution is unique.

notedscholarDecember 11th, 2008 - 12:54

But how will you know if it is done by a computer or not?

NS

http://sciencedefeated.wordpress.com/

SolDecember 11th, 2008 - 12:56

The winning entry has to demonstrate how they got their solution. They must show their work.

notedscholarDecember 15th, 2008 - 16:39

Um hello. I think computers know how to show their work!

NS

http://sciencedefeated.wordpress.com