What is the answer to the 1000 Locker problem?

What is the answer to the 1000 Locker 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.

What is the pattern in locker problem?

That same pattern continues for all 100 students. 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. Cool, huh?

Which lockers will be open at the end?

Locker 1, which has one factor, will clearly be open at the end, since the only student who touches it is the first student, who opens it. Locker 2, with two factors, will be closed, since the only two students to touch it are student 1, who opens it, and then student 2, who closes it.

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.

What numbers are a perfect square?

The first 12 perfect squares are: {1, 4, 9, 25, 36, 49, 64, 81, 100, 121, 144…} Perfect squares are used often in math. Try to memorize these familiar numbers so that you can recognize them as they are used in many math problems.

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. Instead, most colleges have smaller parties through an organization at the college.

Can you open a locker by hitting it?

A jammed locker is a nuisance and a time stealer, but you don’t need to make yourself late. Knocking that item free is often enough to open up the average school locker. If your locker has a key lock, clean it before attempting to force it open.

What is the idea of the locker problem?

The idea is that each person opens or closes only the lockers that are a multiple of his number: #2 changes the multiples of 2, #3 changes the multiples of 3, and so on up to person x, the last one to go through.

How is locker 24 an example of a locker prank?

Let’s take an example of locker 24. Student 1 will open it, since student 1 opens every locker. Student 2 will then close it, since student 2 closes every even locker and 24 is even. Student 3 will open it and then student 4 will shut it, since 24 is a multiple of both 3 and 4. Student 5 will pass it by since 24 is not a multiple of 5.

What are the numbers that are left open in a locker?

Factors are only ever paired with themselves in the case of perfect squares, which means that perfect squares are the only numbers with an odd number of factors! Therefore, the lockers that are left open are: 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.

How does the status of a locker change?

This example makes it clear that each student will change the status of all lockers that have a number that is a multiple of the student’s number. Conversely, every locker will have its status changed by the students that are numbered by one of the locker’s factors.