Unlocking Your Bike the Easy Way

TL;DR

This paper investigates the minimal number of steps needed to open a bicycle combination lock by turning adjacent dials, providing an elementary solution and exploring its relation to a variation of multivariate functions.

Contribution

It introduces a novel analysis of the minimal steps to unlock a combination lock with adjacent dial turns, connecting it to a variation of multivariate functions.

Findings

Derived the minimal number of steps required to unlock the lock

Established a relationship between lock unlocking steps and multivariate functions

Provided an elementary method for solving the problem

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.