In the luminous mechanism of the figure, each of the eight buttons can light up in green or blue. The mechanism works as follows: when turned on, all buttons light up blue, and if we press a button, that button and its neighbors switch colors. If we turn on the mechanism and successively press buttons 1, 3, and 5, how many green lights will be on at the end?

![](https://cdn.mathpix.com/cropped/2024_05_01_dbce7bc2a200e234c3e2g-04.jpg?height=407&width=415&top_left_y=371&top_left_x=1321)
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
The correct answer is (C).

The table shows the color of each button at each step.

|  | $\mathbf{1}$ | $\mathbf{2}$ | $\mathbf{3}$ | $\mathbf{4}$ | $\mathbf{5}$ | $\mathbf{6}$ | $\mathbf{7}$ | $\mathbf{8}$ |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| start | blue | blue | blue | blue | blue | blue | blue | blue |
| pressing button 1 | green | green | blue | blue | blue | blue | blue | green |
| pressing button 3 | green | blue | green | green | blue | blue | blue | green |
| pressing button 5 | green | blue | green | blue | green | green | blue | green |

Therefore, the buttons that ended up with green lights on are $1,3,5,6$ and 8, giving us a total of 5 buttons.