Unlocking Your Bike the Easy Way

Abstract

Combination locks are widely used to secure bicycles. We consider a combination lock consisting of adjacent rotating dials with the first nonnegative integers printed on each of them. Assuming that we know the correct combination and we start from an incorrect combination, what is the minimal number of steps to arrive at the correct combination if in each step we are allowed to turn an arbitrary number of adjacent dials once in a common direction? We answer this question using elementary methods and show how this is related to a variation of (multivariate) functions.

MSC:

• 90C27

ACKNOWLEDGMENT

The author wishes to acknowledge the support of the Austrian Science Fund (FWF) through Project F5513-N26, which was a part of the Special Research Program Quasi-Monte Carlo Methods: Theory and Applications, and Project P32405 Asymptotic geometric analysis and applications.

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the author.

Additional information

Funding

The author wishes to acknowledge the support of the Austrian Science Fund (FWF) through Project F5513-N26, which was a part of the Special Research Program Quasi-Monte Carlo Methods: Theory and Applications, and Project P32405 Asymptotic geometric analysis and applications

Notes on contributors

Mathias Sonnleitner

MATHIAS SONNLEITNER received his Ph.D. in mathematics from University of Passau, Germany, in 2022. Currently, he works there as a postdoc researching in functional analysis, in particular on topics in high-dimensional geometry and information-based complexity.