1. You can find a pattern.

First bright, second dark, third dark, fourth bright, fifth dark, sixth dark, seventh dark, eighth dark, ninth bright, tenth dark, eleventh dark, twelfth dark, thirteenth dark, fourteenth dark, fifteenth dark and sixteenth dark. . . . . . .

After observation, it is found that 1, 4 and 16 are all perfect squares, and there are 10 perfect squares from one to one hundred, so the answer is 10.

2. After further thinking, we can find that if the number of factors of a number is even, the state is dark after 100 seconds, and if the number of factors of a number is odd, the state is bright after 100 seconds, but only the number of factors of a complete square number is odd, so the answer is 10.