Five pillars are arranged in a circle, and between every pair of pillars is a st

Question

Five pillars are arranged in a circle, and between every pair of pillars is a string with a light bulb on it. You are allowed to make the following move, as many times as you want: pick three pillars, then turn the three light bulbs on the strings connecting those pillars on (if they're off or off (if they're on). For example, if you pick the top three pillars in the picture on the left, you would end up with the picture on the right. In the beginning, one light bulb is on and all the rest are off. Is it possible to turn all the light bulbs off?

Explanation / Answer

No, It is not possible since the number of pillars are 5 and number of bulbs are 10. Initially one out of 10 bulbs is On and 9 bulbs out of 10 are Off. For every bulb changing its state, the other two bulbs will also change its state. Thus all the bulbs with same state can only be achieved if total number of bulbs in one particular state is even.

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