Created
February 1, 2025 16:13
-
-
Save przadka/a3b44a9f8c36b96764b617cb3ccc238e to your computer and use it in GitHub Desktop.
o3-mini-maze
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
<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**. |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment