## Monday Math Madness #15

Blinkdagger announced the winner to MMM #14 and now we're on to MMM #15.

Today's puzzle comes from Sameer Shah. He submitted it for MMM #13. Even though it's not the one we picked for that contest, I liked the puzzle and decided to use it for this contest. I'll be sending Sameer a small gift as a token of my appreciation for presenting me with this nice problem. Here's Sameer's problem description, slightly modified:

This problem comes from my time at mathcamp, one summer over a decade ago. It seems in the same spirit that other Monday Math Madness problems are. Most importantly, I think that the variety of different approaches to this problem will be really cool to check out.

You want to find a set of positive integers which add up to 2008, but which yield the largest product. What is the prime factorization of this largest product?

I have a Rubik’s Revolution, courtesy of Techno Source (or $10 Amazon.com gift certificate) to give to the winner. I’ll give more than one prize if I get lots of correct submissions.

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, September 23, 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, September 26, 2008.
- The winner (or winners) will receive a Rubik’s Revolution or a $10 gift certificate to Amazon.com. 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.

MgcclSeptember 15th, 2008 - 13:34

haha, the number 2008. I’m quite burned out by that number on the recent iTest.

DeniseSeptember 24th, 2008 - 07:51

Oh, shoot! I solved this one, but my computer crashed, and in trying to get through daily life on a borrowed computer (without messing up the other person’s desk), all sorts of things are falling through the cracks. I missed the deadline. Ah, well. I never win anyway…but thanks for the fun puzzle!

Tom RossNovember 17th, 2008 - 19:29

9^222*10=largest value

Prime factorization is

2*(3^444)*5