Locker Problem

LOCKER PROBLEM

By David Torres

The first student opened every locker, and all of the lockers were opened. Next came the next student and closed every other locker. Now there were 500 lockers open and 500 lockers closed. The next student came and opened every third locker, and it kept going until 1000 students touched the lockers. The solution was 31 lockers opened. This happened because there was a pattern; the pattern was that every perfect square stayed opened.

This was because the perfect squares had a odd number of factors, and the other ones that were clothes had an even number of factors.

Explanation to chart:

Locker number 4 was touched 3 times by students 1, 4, and2

-This means that it was a perfect square.

Locker number 10 was touched 4 times by students 1, 10, 2, and 5

- This was because it touched with an even number of factors.

Locker number 9 was touched 3 times by students 1, 9, and 3

- This was because it touched with an odd number of factors.