Question

A set of 100 open lockers are numbered from 1 - 100. Sarah comes by and closes all the lockers with even numbers. Then Sarah walks past the lockers again and checks the ones numbered with multiples of 3. If the locker is closed, she opens it; if it is open, she closes it. She repeats this with the multiples of 4, 5, 6, … and so on to 100. When she has finished, which lockers will be open? Explain how you know.

Answer 1

all square numbers such as 1,4,9,16,25,36,49,64,81,100,121,....625,676,729,784,841,900,961.