Pi Mu Epsilon - Math Problem of the Week

Pi Mu Epsilon

Problem of the Week

2/10/2014 due 2/17/2014

Problem No. 4 (Spring 2014)

A sheet of paper contains the numbers 2014; 2015; 2016; ...2113. Suppose you play the following game on this list of numbers. At each stage, you pick two of the numbers on the list, say a and b, cross these out, and replace them by the single number ab + a + b. You keep doing this until only a single number is left (which happens after 99 such moves). Determine, with proof, what this last number is.

Please submit solutions on the table in the Math Lounge C-108. Please include your name and year on your answer. Dr. Roth will verify submitted solutions and a correct submission will be posted on the Math board.A $5 sheetz gift card will be awarded to one correct solution.

posted on 02/11/2014 by lesioa10

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