The Locker Problem

Shane Saour

10/1/09

Locker problem

When the first kid walked buy and opened all the lockers the second kid closed every other one. The third kid touched every third locker and etc. until 1000 kids go through the lockers. For example the sixths locker was touched four times it ends in a closed state and we know this because six has 4 factors. And the fourth locker has 3 factors. The factors for 4 are 1, 4, and 2. You can’t count the same factor twice.

1.O 1x1 1 factor	2.O C 2x1 2 factors	3.O C 1x3 2 factors	4.O O C 1x4 2x2 3 factors	5.O C 1x5 2 factors
6.O O C C 1x6 2x3 4 factors	7.O C 1x7 2 factors	8.O O C C 1x8 4x2 4 factors	9.O O C 1x9 3x3 3 factors	10.O O C C 1x10 2x5 4 factors
11.O C 1x11 2 factors	12.O O O C C C 1x 12 6x2 3x4 6 factors	13.O C 1x13 2 factors	14.O O C C 1x14 7x2 4 factors	15.O O C C 1x15 3x5 4 factors

16.O O O C C 1x16 8x2 4x4 5 factors

There are 31 perfect squares out of all the lockers. All perfect squares have an odd number of factors.

1. How many lockers are open?

31 lockers

We now this because there is 31 perfect squares within 1,000

2. Witch ones are going to be open.

1,4,9,16,25,ect…..,961 the lockers that are left open are going to be perfect squares.

3. Why do perfect squares have an odd number of factors.

Because you can only count one of the repeating factors.

3a.Why is this significant in the solution?

If the lockers have an odd number of factors then it will be left open