Monday Math Madness!

Thanks to our Sponsor!

Welcome to Monday Math Madness! Before we introduce the problem for this week, we would like to take some time to thank our great sponsor, The Art of Problem Solving.

The Art of Problem Solving offers a challenging curriculum in problem solving mathematics for strong math students in grades 6-12. The bookstore also offers a variety of other books from prominent competitions, such as MOEMS, MATHCOUNTS, and the AMC. If you think the problems that you find here are fun, there are books at their website filled with countless problems that will keep your mind buzzing for years.

The people at The Art of Problem Solving have been kind enough to provide 25 dollar gift certificates to the winners of this contest. See the Rules sections for more details! Without further ado . . . let the games begin!

Blinkdagger Burgers

Part I : The Secret Sauce

The latest craze in the fast food community is the emergence of Blinkdagger Burgers. They use only fresh ingredients and cook the meat to perfection. But what really sets them apart from their competitors is the secret sauce.

The secret sauce is produced every Monday in a factory overseas in Austrailia. Nortrom, the janitor of the factory, is responsible for creating the sauce and then shipping it to all of the branch restaurants because the manager is out sick. Before the manager left however, he provided specific instructions on how to create the secret sauce:

Start with 500 gallons of mayonaise.

1) Mix in 10 gallons of ketchup. Stir until completely mixed.

2) Remove 10 gallons of the mixture.

3) Repeat steps 1 and 2 until the mixture is approximately 50% mayonaise and 50% ketchup.

How many interations will it take to create the secret sauce?

Part II : Counting Burgers

Due to Nortrom’s success in creating the secret sauce, he was named as the employee of the month. At Blinkdagger Burgers, the employee of the month gets to eat as many burgers as he (or she) pleases. Note that Blinkdagger Burgers only serves two types of burgers: a single burger (1 lb) and a double burger (2 lbs).

The following tuesday, Nortrom decides that he wants to eat 3 lbs of beef. Being the savvy mathematician that he is, Nortrom immediately notices that are three different ways that he can accomplish this:

1) he can eat 3 single burgers
2) he can start off with a double burger, and end with a single burger
3) he can start with a single, and end with a double

On Wednesday, Nortrom decides that 3 lbs of beef was far too little. He instead aims for 17 lbs of beef. After thinking for a couple minutes, Nortrom concludes that there are X different ways he can accomplish this.

On Thursday, Nortrom decides he wants to try to eat 25 lbs of beef. He quickly realizes that there are Y different ways that he can accomplish this.

What are X and Y?

The Rules

  1. There will be a winner for both Part 1: The Secret Sauce and for Part 2: Counting Burgers, giving you two chances to win! Part II is a little trickier, so good luck! If you want to submit an answer to both problems, please do so in separate emails.

  2. Email your answers to mondaymathmadness at gmail dot com.

  3. The winner from both Part I and Part II will receive a $25 gift certificate to use at the bookstore from the Art Of Problem Solving.

  4. Depending on how many submissions we receive (we are aiming for 200), we will be giving out additional prizes, giving you yet more chances to win. We’d also like to give a prize out to the “best” or “most creative” answer. These prizes will consist of a 10 dollar gift certificate to Amazon.com or this spiffy Rubik’s Cube (the cube is only available to US participants and is not the traditional rubik’s cube that we all grew up with).

    Rubik's Cube

  5. Inelgible for any one person to win more than once per year. But you should still submit your answer!

  6. Answer must be explained. You must show your work! We will accept answers in the form of a MATLAB script as well. We will be the final judge on whether an answer was properly explained or not.

  7. The deadline to submit answers is May 20th 2008, Tuesday 12:00 AM Pacific Standard Time

  8. The winners will be chosen randomly from all the submittals using a random number generator.

  9. The winner will be announced at 9:00 AM PST May 23th, 2008.

  10. Comments for this post should only be used to clarify the problem. Please do not discuss ANY potential solutions.

  11. Please spread the word about our contest! We’re aiming for 200 submissions for this contest. If we meet 200, we will announce two winners! So please stumble this post or advertise by word of mouth!