Title

Custom Locks: Counting the Combinations

Date

5-30-2013 9:00 AM

Location

Math and Nursing Building (MNB) 103

Department

Mathematics

Session Chair

Breeann Flesch

Session Title

Mathematics Senior Project Presentations 1

Faculty Sponsor(s)

Breeann Flesch

Presentation Type

Symposium

Abstract

Counting the possible entries in a combination lock is trivial when we recognize that any lock with buttons 1 to n will have precisely n! combinations. In this presentation, we will explore the different methods of counting combinations when the buttons on our lock can be pushed simultaneously. Using recurrence relations and generating functions to derive formulas, we see that it is possible to count the number of combinations of any such lock with buttons 1 to n.

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May 30th, 9:00 AM

Custom Locks: Counting the Combinations

Math and Nursing Building (MNB) 103

Counting the possible entries in a combination lock is trivial when we recognize that any lock with buttons 1 to n will have precisely n! combinations. In this presentation, we will explore the different methods of counting combinations when the buttons on our lock can be pushed simultaneously. Using recurrence relations and generating functions to derive formulas, we see that it is possible to count the number of combinations of any such lock with buttons 1 to n.