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February 1, 2025 16:44
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flash-maze
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<USER> | |
### 3. In the Maze | |
In the maze, the rooms are numbered from 0 to 15. Moving between rooms triggers an alarm, except when: | |
- Moving to a room with a number exactly 3 greater than the current room, or | |
- Moving to a room with a number exactly 13 less than the current room. | |
We enter the maze through room number 0 and exit through room number 1. | |
**How many rooms will we pass through (including rooms 0 and 1) if we never trigger the alarm along the way?** | |
#### Maze Layout: | |
``` | |
9 12 15 2 | |
6 7 4 5 | |
3 10 11 8 | |
0 13 14 1 | |
``` | |
<ASSISTANT> | |
Let's trace a possible path through the maze, ensuring we don't trigger the alarm: | |
1. **Start at room 0.** | |
2. **Move to room 3:** This is allowed because 3 = 0 + 3. | |
3. **Move to room 6:** This is allowed because 6 = 3 + 3. | |
4. **Move to room 9:** This is allowed because 9 = 6 + 3. | |
5. **Move to room 12:** This is allowed because 12 = 9 + 3. | |
6. **Move to room 15:** This is allowed because 15 = 12 + 3. | |
7. **Move to room 2:** This is allowed because 2 = 15 - 13. | |
8. **Move to room 5:** This is allowed because 5 = 2 + 3. | |
9. **Move to room 8:** This is allowed because 8 = 5 + 3. | |
10. **Move to room 11:** This is allowed because 11 = 8 + 3. | |
11. **Move to room 14:** This is allowed because 14 = 11 + 3. | |
12. **Move to room 1:** This is allowed because 1 = 14 - 13. | |
So, the path is 0 -> 3 -> 6 -> 9 -> 12 -> 15 -> 2 -> 5 -> 8 -> 11 -> 14 -> 1. | |
We pass through 12 rooms in total. |
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