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The Tradition of Sharing

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Authors:
Anany Levitin
Chapter:
Introduction
Exercise:
1.1 Exercise
Question:12 | ISBN:9780132316811 | Edition: 3

Question

Locker doors There are n lockers in a hallway, numbered sequentially from 1 to n. Initially, all the locker doors are closed. You make n passes by the lockers, each time starting with locker #1. On the ith pass, i = 1, 2, . . . , n, you toggle the door of every ith locker: if the door is closed, you open it; if it is open, you close it. After the last pass, which locker doors are open and which are closed? How many of them are open?

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