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 faculty judge, 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.
Solutions Due: Friday, September 29, 5:00 p.m.
Send solutions to bkennedy@gettysburg.edu.
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. Weekly winners will receive a POW victory button, and the best-performing students of the semester will receive the Paul Mugabi problem-solving award.
Mysteries of the Pyramids
A Lockridge Pyramid is a triangular array of numbers where each entry (except in the bottom row) is the sum of the two entries below it. Example:
20
9 11
3 6 5
2 1 5 0
Question: how many Lockridge pyramids are there so that:
- the bottom row consists of only 0s and 1s; and
- the number at the top of the pyramid is 10?
Answer, and explain!
