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Mathematical calculation of switch state of 200 lamps
The square root is a positive integer within 200! This problem is to investigate the parity of each factor of 1~200. The lamp state with odd factor is different from the initial state. On the contrary, the lamp state remains unchanged when the factor is even. Give two examples: No.2 light has two factors (2 = 1 and 2), so it is switched on and off twice, and the state remains unchanged; There are three factors in the No.4 light: 1, 2, 4, (4= 14=22) press it three times, which is different from the initial state, that is, the light is off at first, and it will light up after pressing it three times.

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