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February 1, 2025 15:59
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4o-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> | |
To solve this, we'll identify the sequence of rooms starting from room **0** and ending at room **1**, while following the rules that prevent triggering the alarm: | |
### **Allowed Moves:** | |
1. Move to a room **exactly 3 greater** than the current room. | |
2. Move to a room **exactly 13 less** than the current room. | |
### **Step-by-step Pathfinding:** | |
- **Starting Room: 0** | |
- Move to **0 + 3 = 3** (valid move, no alarm). | |
- From **3**, move to **3 + 3 = 6** (valid). | |
- From **6**, move to **6 + 3 = 9** (valid). | |
- From **9**, move to **9 + 3 = 12** (valid). | |
- From **12**, move to **12 + 3 = 15** (valid). | |
- From **15**, move to **15 - 13 = 2** (valid). | |
- From **2**, move to **2 + 3 = 5** (valid). | |
- From **5**, move to **5 + 3 = 8** (valid). | |
- From **8**, move to **8 + 3 = 11** (valid). | |
- From **11**, move to **11 + 3 = 14** (valid). | |
- From **14**, move to **14 - 13 = 1** (valid). | |
### **Rooms Visited:** | |
0 → 3 → 6 → 9 → 12 → 15 → 2 → 5 → 8 → 11 → 14 → 1 | |
This path includes **12 rooms** in total. | |
**Final Answer:** ✅ **12 rooms** (including rooms 0 and 1). |
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