# Find the number of Lights.

**Number Theory**Level 3

The students of a Technical Institute went to the house of bulb collector Prof Sharma. He gave them a task- Each of them had to go and switch on bulbs that were switched off and switch off the on ones. At the start, all lights were switched off. They had to proceed in the following manner-

1. The first student switched on all lights.

2. The second one switches off all switches that are multiples of two.

3. The third one switched off all on lights and switched on the off lights that were multiples of 3.This continued for 4, 5, 6 and so on.

1. The first student switched on all lights.

2. The second one switches off all switches that are multiples of two.

3. The third one switched off all on lights and switched on the off lights that were multiples of 3.This continued for 4, 5, 6 and so on.

If the professor had 1000 bulbs and each of the 1000 students did as told, find the number of bulbs that remained on after the exercise.

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