Locker Problem Sheet With Answers printable pdf download

Locker Problem Sheet With Answers

Locker Problem

– Answer Key

Name_____________________

One hundred students are assigned lockers 1 through 100. The student assigned to

locker number 1 opens all 100 lockers. The student assigned to locker number 2 then

closes all lockers whose numbers are multiples of 2. The student assigned to locker

number 3 changes the status of all lockers whose numbers are multiples of 3 (e.g.

locker number 3, which is open gets closed, locker number 6, which is closed, gets

opened). The student assigned to locker number 4 changes the status of all locker

whose numbers are multiples of 4, and so on for all 100 lockers.

1. Which lockers will be left open?

1, 4, 9, 16, 25, 36, 49, 64, 81, 100

2. Explain how you determined that these particular lockers will be open.

Either by looking at a pattern with the opened and closed lockers…open, 2

closed, open, 4 closed, open, 6 closed, open, 8 closed, open….

Noticing that the lockers opened are perfect squares

Other?

3. What do you notice about these particular locker numbers?

The locker numbers are perfect squares.

4. Why are these specific locker numbers still open?

They have an odd number of factors.

5. How many lockers, and which ones, were touched exactly twice? How do you

know?

25; 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73,

79,83, 89, 97; they are the prime numbers which only have two factors.

6. Which students touched both lockers 36 and 48? How do you know?

Locker Problem Sheet With Answers