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What is the answer to the 1000 lockers problem?

What is the answer to the 1000 lockers problem?

Solution: 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.

Why are locker numbers that are perfect squares the only ones that remain open?

A number only has an odd number of factors if one of the factor pairs is two of the same number, so perfect squares. Which lockers will remain open then? Even numbered lockers that are perfect squares and odd numbered lockers that are not perfect squares. There are 500 even and 500 odd numbers between 1 and 1000.

How do you do locker problems?

The Locker Problem Imagine 100 lockers numbered 1 to 100 with 100 students lined up in front of those 100 lockers: The first student opens every locker. The second student closes every 2nd locker. The 3rd student changes every 3rd locker; if it’s closed, she opens it; if it’s open, she closes it.

Why do lockers have vents?

Ventilation and Hygiene 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.

Why should we have lockers?

Lockers give students a place to store their belongings in between classes without the risk of them being tampered with or stolen. In class, bags are out in the open and are an easy target to drop things into, like a tracking device or an incriminating item that could get the innocent student into trouble.

What is a square root of 1000?

The value of the square root of 1000 is approximately equal to 31.622.

What is the first perfect square after 1000?

They are 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900 and 961.

What is the standard size of a locker?

24″ Wide Standard Gear Lockers are constructed of 16 gauge steel, are 6 feet high, 24″ deep and are available in gray, tan or blue finish.

What is a school locker?

A locker is a home base for not only schoolwork, but a social spot for friends, the one place where students know that they and their belongings are secure. From hallway lockers to locker rooms, from preschool through college, we have every kind of locker for school that you could possibly need.

Why do we need lockers in school?

What is a cube root of 1000?

The cube root of 1000 is the number which when multiplied by itself three times gives the product as 1000. Since 1000 can be expressed as 2 × 2 × 2 × 5 × 5 × 5. Therefore, the cube root of 1000 = ∛(2 × 2 × 2 × 5 × 5 × 5) = 10.