Problem of the Week: Splitting Up

By Department of Mathematics

Editor’s Note: The Department of Mathematics at Gettysburg College hosts a problem of the week challenge to determine each semester’s Paul Mugabi problem-solving award recipient(s).  Each week’s entries are scored by a panel of faculty judges, and winner(s) from each week will receive a Problem Of the Week (P.O.W.) button.  The Gettysburgian is not involved in or responsible for accepting or evaluating students’ submissions to this contest.

THE RULES:

The contest is open to all Gettysburg College students. Up to three people may work together on a submission. Make sure your name is on your submission and that any sources are properly cited!  Send solutions to bkennedy@gettysburg.edu or put solutions in the marked envelope in the hallway outside Glatfelter 215.  This problem was posted on Friday, October 26 and solutions are due on Friday, November 2 by 5:00 p.m.

THE PROBLEM: 

Divide the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 into two sets, S and P, in such a way that the sum of the numbers in S is equal to the product of the numbers in P. (Each of the numbers 1,…,10 must be in exactly one of the sets S or P. Consider the product of a single number to be that number itself.)

Challenge 1: Find a solution. Challenge 2: Find more than one solution. Challenge 3: Find all solutions, and explain how you know that your list of solutions is complete.

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Author: Gettysburgian Staff

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