# So many lights

**Number Theory**Level 3

In a hall in a school there are 100 light bulbs labelled from 1 to 100 and their switches are also numbered accordingly.100 students enter the hall one by one.each student operates the switch(es) whose number is a multiple of his order of entering the hall.provided all switches were initially off,how many bulbs will be on after all students have entered?

**For example:** The student who enters at number 1 will on all the switches.student no.2 will off switches with no. 2,4,6,8......98,100.and so on.

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