# Locker doors

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

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#### 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.