1000 Students - Odd Lockers Open

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In summary, after recess, the 1000 students of a school lined up and entered the school in a specific order where each student had a task related to the lockers. As a result, all the square numbers between 1 and 1000 were left open.
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vivalajuicy
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Following recess, the 1000 students of a school lined up and entered the school as follows: The first student opened all of the 1000 lockers in the school. The second student closed all lockers with even numbers. The third student “changed” all lockers that were numbered with multiples of 3 by closing those that were open and opening those that were closed. The fourth student changed each locker whose number was a multiple of 4 and so on. After all 100 students had entered the building in this fashion, which lockers were left open?
 
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  • #2
Re: word problem for my math assignment

I think you mean after 1000 students. If so, the answer is all the square numbers between 1 & 1000.
 

FAQ: 1000 Students - Odd Lockers Open

What is the purpose of the "1000 Students - Odd Lockers Open" experiment?

The purpose of this experiment is to determine the pattern of which odd-numbered lockers will be open after 1000 students have opened and closed them according to a specific set of rules.

How is the experiment conducted?

The experiment is conducted by having 1000 students follow a set of rules to open and close odd-numbered lockers. The first student will open all lockers, the second student will close every other locker, the third student will toggle every third locker, and so on until the 1000th student. The end result will show which lockers are open.

What is the expected outcome of the experiment?

The expected outcome is that only the lockers whose numbers are perfect squares (1, 4, 9, 16, etc.) will be open after all 1000 students have completed their task.

What is the significance of this experiment?

This experiment helps to demonstrate a basic mathematical concept known as the "Sieve of Eratosthenes". It also highlights the concept of perfect squares and their patterns.

Can this experiment be replicated with different numbers of students and lockers?

Yes, this experiment can be replicated with any number of students and lockers, as long as the number of students is equal to the number of lockers. The same pattern will emerge with the perfect squares being the only open lockers.

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