Puzzle - Light Bulb Switching
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Light Bulb Switching Teaser
The title of this quesion is easy to understand.
There are 100 light bulbs with label 1 to 100. At the very beginning, there are all off.
In the 1 pass, all the bulbs whose label is multiple of 1 will be switched. (so after first pass, all the bulbs will be on)
In the 2 pass, all the bulbs whose label is mulitple of 2 will be switched.
…
So on so force, in the 100 pass, the last bulb will be switched.
The quesion is after 100 pass, how many bulbs will be on, what’s the labels of these bulbs?
The anwer is 10. The labels are 1 4 9 16 25 36 49 64 81 100 respectively.
Explain:
According to question, the bulb which is switched odd numbers can be on at last.
So the label or id of these bulbs with odd numbers of factors will satisfy above condition. What kind of number from 1 - 100 has odd numbers of factors?
The answer is obvious. The quadratic components.
1^2, 2^2, 3^2, … , 10^2.
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