A1. A traffic light alternates between green and red at regular intervals. The green and red periods last the same amount of time, always 1, 2, or 3 minutes. There are four color combinations for the light at the times 12:08 and 12:09: red-red, red-green, green-red, and green-green. How many of the four combinations are possible given that the light was red at exactly 12:05 and also red at exactly 12:12?
A) 1
B) 2
C) 3
D) 4
E) The light cannot be red at both 12:05 and 12:12.
A1. B) 2

Given that the traffic light is red at 12:05. For a traffic light of period 1, the colors for the times 12:05 to 12:12 are fixed, alternating between red and green. For period 2, there are two possibilities, and for period 3, there are three possibilities:

| period | 12:05 | 12:06 | 12:07 | 12:08 | 12:09 | $12: 10$ | $12: 11$ | $12: 12$ |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| 1 min | red | green | red | green | red | green | red | green |
| $2 \mathrm{~min}$ | red | red | green | green | red | red | green | green |
| $2 \mathrm{~min}$ | red | green | green | red | red | green | green | red |
| $3 \mathrm{~min}$ | red | red | red | green | green | green | red | red |
| $3 \mathrm{~min}$ | red | red | green | green | green | red | red | red |
| $3 \mathrm{~min}$ | red | green | green | green | red | red | red | green |

Of these six possibilities, three meet the condition that the light is red at 12:12. For the times 12:08 and 12:09, this results in two color combinations: red-red and green-green.