Wild About Math! Making Math fun and accessible

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:

1. Email your answers with solutions to mondaymathmadness at gmail dot com.
2. Only one entry per person.
3. Each person may only win one prize per 12 month period. But, do submit your solutions even if you are not eligible.
4. 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.
5. 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.)
6. The winner will be chosen randomly from all timely well-explained and correct submissions, using a random number generator.
7. The winner will be announced Friday, September 26, 2008.
8. 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.
9. Comments for this post should only be used to clarify the problem. Please do not discuss ANY potential solutions.
10. 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.