Light bulbs are numbered 1 to 100, and kept off initially. When the first person comes in, he switches all bulbs to on where the number are multiples of one (so, all bulbs). The second person switches all bulbs where the numbers are multiples of two (so, 2, 4, 6, 8, etc). The third person switches all bulbs where the numbers are multiples of three (so, 3, 6, 9, 12, etc). This process continues until one hundred persons pass. After this, how many bulbs are ON?

With such a question, start running the job for a smaller number of people and check if you recognize a pattern. Let's slim it down to 20 people. Every bulb whose number is a perfect square will be switched on, and the rest will remain off. Thus, the bulbs 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100 are ON, at the end. Hence 10 bulbs are on.

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