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# Locker doors

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6. Students at an elementary school tried an experiment. When recess was over, each student walked into the school one at a time. The first student opened all the first 100 locker doors. The second students closed all the locker doors with even numbers. The third student changed all the locker doors with numbers that were multiples of three (change means close the open doors and open the closed doors). The fourth student changed all dors numbered with multiples of four; the fifth student changed all doors that were multiples of five, and so on. After 100 sutdents had entered the school, which locker doors were open? There is a pattern

https://brainmass.com/math/discrete-math/locker-doors-67232

#### Solution Preview

There is indeed a pattern
After 25 students have been through with the exercise
All lockers with numbers 1,4,9,16,25 are open and others are closed
These are squares of 1,2,3,4,5 respectively

1^ 2 =1 (^ stands for power)
2 ^2 =4
3^2=9
4^2 =16
5^2 =25

After 100 students had entered the school, the locker doors that were open: 1,4,9,16,25,36,49,64,81,100
i.e. squares of 1,2,3,4,5,6,7,8,9,10

There is a logic behind it
The 1st ...

#### Solution Summary

Finds out which locker doors are open.

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## Number Patterns : Door Problem

A school had a very unusual tradition involving its 1000 students and its 1000 lockers. On opening day, after the head of the school had closed all the lockers, a student walked by and opened every single one. A second student then closed every second one (#2, 4, 6, 8 etc). A third student then changed every third locker (#3,6,9,12 etc), that is, she opened the ones that were closed and closed the ones that were open. A fourth student then changed every fourth locker, after which a fifth student changed every fifth locker , and so on until all 1000 students had passed by all 1000 lockers. At the end of this strange activity, which lockers were open?

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