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Created February 1, 2025 16:13
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o3-mini-maze
<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>
We are only allowed to move in one of two ways:
- **Add 3:** Move from room \(X\) to room \(X+3\).
- **Subtract 13:** Move from room \(X\) to room \(X-13\).
However, the move is only permitted if the resulting room number is between 0 and 15 (inclusive).
### Step-by-Step Path
1. **Start at Room 0:**
Allowed move: \(0 + 3 = 3\).
**Path so far:** 0 → 3
2. **From Room 3:**
Allowed move: \(3 + 3 = 6\).
**Path:** 0 → 3 → 6
3. **From Room 6:**
Allowed move: \(6 + 3 = 9\).
**Path:** 0 → 3 → 6 → 9
4. **From Room 9:**
Allowed move: \(9 + 3 = 12\).
**Path:** 0 → 3 → 6 → 9 → 12
5. **From Room 12:**
Allowed move: \(12 + 3 = 15\).
**Path:** 0 → 3 → 6 → 9 → 12 → 15
6. **From Room 15:**
The \(+3\) move would give 18, which is out of range, so we must use the \(-13\) move:
\(15 - 13 = 2\).
**Path:** 0 → 3 → 6 → 9 → 12 → 15 → 2
7. **From Room 2:**
Allowed move: \(2 + 3 = 5\).
**Path:** 0 → 3 → 6 → 9 → 12 → 15 → 2 → 5
8. **From Room 5:**
Allowed move: \(5 + 3 = 8\).
**Path:** 0 → 3 → 6 → 9 → 12 → 15 → 2 → 5 → 8
9. **From Room 8:**
Allowed move: \(8 + 3 = 11\).
**Path:** 0 → 3 → 6 → 9 → 12 → 15 → 2 → 5 → 8 → 11
10. **From Room 11:**
Allowed move: \(11 + 3 = 14\).
**Path:** 0 → 3 → 6 → 9 → 12 → 15 → 2 → 5 → 8 → 11 → 14
11. **From Room 14:**
The \(+3\) move would give 17 (invalid), so we use the \(-13\) move:
\(14 - 13 = 1\) (the exit room).
**Path:** 0 → 3 → 6 → 9 → 12 → 15 → 2 → 5 → 8 → 11 → 14 → 1
### Count the Rooms
Including both the starting room (0) and the exit room (1), the path passes through:
\[
12 \text{ rooms.}
\]
Thus, if we never trigger the alarm, we will pass through **12 rooms**.
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