Math Problem of Month

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Department of Mathematics and Actuarial Science

Math Problem of the Month
Competition

Any IUN student is eligible to participate. Others may apply to be accepted as participants. Participants may consult any written source, but must document that source. Participants may speak to any other eligible participants, but must document their conversations. Each problem is worth 5 points. The participant who accumulates the most points by the end of March wins the contest and cash prize.

Check Scorecard.

March 2008 Problem The four-color theorem says that if states/nations are contiguous, only 4 colors are required in order to color each state/nation on a map a different color so that no two neighboring states/nations are the same color. (This theorem was long known to mapmakers but was only proven in 1976.) Draw an example of fictitious states to show that 3 colors will not suffice. Turn in your solutions (not just answers!) to Dr. Caithamer HH433 by March 31. Each problem is worth 5 points. The participant who accumulates the most points by the end of March wins the contest and cash prize.

January 2008 Problem Without reference to the number pi, show that if Circle A has twice the radius of Circle B then Circle A also has twice the circumference of Circle B. (The point of this problem is that the number is introduced as the ratio between the circumference of any circle and its diameter, which is twice its radius. How do we know that this ratio is the same for all circles? Proving that this is true for Circle A and Circle B is the major point in the proof of this general fact.)
November 2007 Problem A ship leaves Oahu and sails 3,000 miles west. The captain then decides he needs to get back to Oahu as quickly as possible. What is the shortest distance he can sail back to Oahu? (Hint: The answer is not 3,000!) Check November Solution

October 2007 Problem

If a pyramid whose base is the shape of an equilateral triangle is built out of billiard balls, and this pyramid has n layers/levels of balls, then how many balls does the entire pyramid contain?

Check October Solution