What is the answer to the 100 Locker problem?

Here’s the question: “Which lockers are left open after all 100 students have walked the row of lockers?” As many of you found, the perfect square lockers (#s 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100) are the only lockers left open.

When all 1000 students have finished which locker doors are open?

The principal only needs to close the lockers whose numbers are perfect squares. This means the solution is as easy as finding the square root of the highest possible perfect square within 1000. Therefore, 31 is the number of lockers the principal has to close.

How do you open a locker without the code?

Pull up gently on the shackle and hold it in place. Turn the dial clockwise listening carefully until you hear the lock click. Start with a good deal of pressure and gently let up as you spin it around, until you meet resistance in only one place. If the dial catches every few numbers, you are pulling too hard.

What are number factors?

The factors of a number are the numbers that divide into it exactly. The number 12 has six factors: 1, 2, 3, 4, 6 and 12. If 12 is divided by any of the six factors then the answer will be a whole number.

What does a factor of 3 mean?

This is described as showing a “fall by a factor of 3”. This phrase doesn’t ring true. If a factor of 3 is a 1/3, then a fall by a third would be down to 2000. So the phrase is meant to represent a fall to a third.

How to do 100 closed lockers in a hallway?

Suppose you’re in a hallway lined with 100 closed lockers. You begin by opening every locker. Then you close every second locker. Then you go to every third locker and open it (if it’s closed) or close it (if it’s open). Let’s call this action toggling a locker. Continue toggling every nth locker on pass number n.

How to know how many lockers are open or closed?

You begin by opening every locker. Then you close every second locker. Then you go to every third locker and open it (if it’s closed) or close it (if it’s open). Let’s call this action toggling a locker. Continue toggling every nth locker on pass number n. After 100 passes, where you toggle only locker #100, how many lockers are open?

How do you do the 100 lockers puzzle?

You are standing in a school hallway lined with 100 closed lockers. You then open all 100 lockers. After this, you then close every 2nd locker (so the 2nd, 4th, 6th…98th and 100th are all closed). Then, you go to every third locker and open it if it is closed or close it if it is open (let’s call this toggling the locker for our discussion).

How many lockers are toggled on pass number 40?

This problem is based on the factors of the locker number. Each locker is toggled by each factor; for example, locker #40 is toggled on pass number 1, 2, 4, 5, 8, 10, 20, and 40. That’s eight toggles: open-closed-open-closed-open-closed-open-closed.

How do you break a lock with a screwdriver?

Use A Screwdriver With your screwdriver, push the button on the door handle and turn. If you are locked out from the outside, seek out a small hole in the doorknob and turn it until it catches into a groove and pops open the door.

Is 6 a multiple or a factor of 12?

The factors of 12 are 1, 2, 3, 4, 6, and 12, because each of those divides 12 without leaving a remainder (or, alternatively, each of those is a counting number that can be multiplied by another counting number to make 12).