# What is the answer to the 1000 lockers problem?

## What is the answer to the 1000 lockers problem?

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 play the Locker game?

The Locker Game

- The first student starts with the first locker and goes down the hallway and opens all the lockers.
- The second student starts with the second locker and goes down the hallway and shuts every other locker.

**What is the Locker game?**

The Locker Game is a mathematical investigation task that allows students to deepen their understanding of factors and multiples of whole numbers. As a classic mathematical puzzle, this task provides opportunities for students to look for and make use of structure in the relationship with factors and multiples.

### Do you get lockers in college?

Though often not as visible as their high school counterpart, most college and university campuses have lockers in at least a few niche locations. Traditionally, campuses have offered a limited number of lockers to be checked out, with or without a fee, for a semester or an academic year.

### Which lockers are open after all 100 students pass through the hallway?

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.

**Why do lockers have vents?**

Ventilation and Hygiene The simple answer to this question, is that lockers have these holes built into them for hygienic purposes. By allowing clean air to circulate into the locker, these vents allow things like sweaty clothes to dry out and prevent unpleasant odours from building up.

#### Do colleges have prom?

Almost all colleges do not have prom. Some smaller colleges might have prom but it’s very rare. There isn’t prom at colleges because they student population is too large. College prom would require an extremely large room and resources to provide for students.

#### Can you solve the locker riddle solution?

You know that these ten lockers are the solution, so you open them immediately and read the words inside: “The code is the first five lockers touched only twice.” You realize that the only lockers touched twice have to be prime numbers since each only has two factors: 1 and itself. So the code is 2-3-5-7-11.

**How do you open a lock without a key?**

Hold the tension wrench twisted in the correct direction and insert the rake into the lock where the teeth of the keys would go. Push and pull the rake out of the lock, twisting it and working by feel. Twist the tension wrench in the correct direction, and the lock should spring open!

## Why does a locker always end up closed?

Combining this knowledge with our other knowledge, we can say that a locker will end up closed if it has an even number of factors, because the number of times a locker is toggled equals the number of factors. If a locker has an odd # of factors, the locker will end up being open.

## How to solve the problem of the locker problem?

The problem begins with the first student opening all 1000 lockers; next the second student closes lockers 2,4,6,8,10 and so on to locker 1000; the third student changes the state (opens lockers closed, closes lockers open) on lockers 3,6,9,12,15 and so on; the fourth student changes the state of lockers 4,8,12,16 and so on.

**Are there 100 lockers that will remain open?**

This would also mean that we would have an odd number of factors – and an odd number of factors would mean that particular locker will remain open. Since there aren’t very many perfect squares between 1 and 100, you can list them out – here they are: 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100 – so, exactly 10 lockers will remain open.

### How do you toggle lockers on pass number n?

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). You proceed to toggle every nth locker on pass number n.