# Lights out

**Number Theory**Level 3

There are 100 bulbs in a hall numbered from 1 to 100 with their switches also numbered accordingly.100 students enter the hall one by one and each student operates the switches whose number is a multiple of his order of entering the hall.If all switches were initially off how many will be on after all students have entered?

**Example:** The student who enters first operates(on) all switches having 1 as a factor. Student no. 2 operates(off) all switches having 2 as a factor.And so on.....

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