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 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 firstname.lastname@example.org 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.
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.