There are $100$ candles which are numbered from 1 to 100.There are 100 students. The 1st student lights up all the candles. The 2nd student changes the state of the candles(lights up or lights off) which are multiples of $2$ . The 3rd student changes the state of the candles(lights up or lights off) which are multiples of $3$ .

This continues till the 100th student.

Find how many candles are still lightened up in the end.

The answer is 10.

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It is same as "How many numbers from 1 to 100 has odd amount of positive divisors?"

All perfect squares has odd amount of positive divisors,so the answer is 1,4,9,...,100,total of 10 candles.