9. A museum has 7 exhibition rooms in a row. The guard starts by walking into the first room, then to the second... and after reaching the seventh room, he turns back, walking to the sixth room, then to the fifth... Each time he enters a room, he toggles the light switch in that room. If all 7 rooms are initially lit, how many rooms will still have their lights on after he has walked into 100 rooms.
【Answer】3
【Analysis】Cycle problem + Parity
Starting from the first room to the seventh room, and then returning to the second room can be seen as a cycle, in which 12 rooms are passed in one cycle. Rooms 1 and 7 have their switches toggled once, while rooms 2 and 6 have their switches toggled twice, meaning that after one cycle, the states of rooms 1 and 7 change once, while the states of rooms 2 and 6 remain unchanged; $100 \div 12=8 \cdots 4,8$ cycles later, all lights are still on;

After passing through 4 more rooms, these 4 rooms will be turned off, therefore, in the end, there are still 3 exhibition rooms with the lights on.