02/07/05 - Problem of the Week (Problems)

The Big Game - The Problems

February 7, 2005

Have you noticed how we never see "Superbowl 39" anywhere? It’s always written with Roman numerals as "Superbowl XXXIX." When it comes to the Superbowl, we’re suddenly comfortable with using Roman numerals. If you are unfamiliar with Roman numerals, there are many Web sites that will take you through the general rules, such as http://www.legionxxiv.org/numerals/. Write down your phone number, including the area code. Now, instead of seeing ten digits, consider your phone number to be two three-digit integers followed by a four-digit integer. Can you write these three integers in Roman numerals. The MATHCOUNTS main number is (703) 684-2828. How would the three integers from this number be written with Roman numerals? (*For folks with an integer greater than 5000, use a V with a line over it to indicate 5000.)

When was the last time you watched a football game's halftime show on television? Most likely it was last year’s Superbowl; it’s just not a common occurrence at any other time. According to the official Superbowl Halftime Honor Roll (http://www.superbowl.com/features/entertainment/halftime-honorroll) , there have been 32 halftime shows requiring a producer. Disney has been listed as the producer of six of these shows. What is the ratio of the number of shows produced by Disney to the number of shows with a different producer? Express your answer as a common fraction.

Superbowl Sunday also brings out eating habits that are only outmatched by those seen on Thanksgiving. Additionally, it’s known to be the biggest party day of the year (outdoing even New Year’s Eve). There are many helpful hints on the Internet to help you plan the perfect party. One recipe for Superbowl popcorn calls for 4 quarts of popcorn, 12 ounces of peanuts and 2 cups of shredded cheddar cheese (http://www.recipesource.com/munchies/snacks/01/rec0158.html). What percent of the mix of these three ingredients does the cheese represent? Express your answer to the nearest tenth. Note: 8 ounces = 1 cup and 4 cups = 1 quart.


	2005 Problems & Solutions Problem of the Week Archive January #1 - Problems / Solutions #2 - Problems / Solutions #3 - Problems / Solutions #4 - Problems / Solutions #5 - Problems / Solutions February #1 - Problems / Solutions #2 - Problems / Solutions #3 - Problems / Solutions #4 - Problems / Solutions March #1 - Problems / Solutions #2 - Problems / Solutions #3 - Problems / Solutions #4 - Problems / Solutions April #1 - Problems / Solutions #2 - Problems / Solutions #3 - Problems / Solutions #4 - Problems / Solutions May #1 - Problems / Solutions #2 - Problems / Solutions #3 - Problems / Solutions #4 - Problems / Solutions #5 - Problems / Solutions June #1 - Problems / Solutions #2 - Problems / Solutions #3 - Problems / Solutions #4 - Problems / Solutions July #1 - Problems / Solutions #2 - Problems / Solutions #3 - Problems / Solutions #4 - Problems / Solutions August #1 - Problems / Solutions #2 - Problems / Solutions #3 - Problems / Solutions #4 - Problems / Solutions #5 - Problems / Solutions September #1 - Problems / Solutions #2 - Problems / Solutions #3 - Problems / Solutions #4 - Problems / Solutions October #1 - Problems / Solutions #2 - Problems / Solutions #3 - Problems / Solutions #4 - Problems / Solutions #5 - Problems / Solutions November #1 - Problems / Solutions #2 - Problems / Solutions #3 - Problems / Solutions #4 - Problems / Solutions December #1 - Problems / Solutions #2 - Problems / Solutions #3 - Problems / Solutions #4 - Problems / Solutions