School bus picks A from his house and takes two left turns and then one right turn to reach his school. If the bus is facing East, while reaching the school, which direction was the bus facing at his home?

Question

Accepted Answer

To determine the direction the bus was facing at A's home, we need to analyze the sequence of turns the bus makes from A's house to the school.

1. **Initial Direction at Home**: Let's assume the bus starts facing a certain direction at A's home. We need to determine this initial direction based on the final direction at the school.

2. **Sequence of Turns**:
   - The bus takes two left turns and then one right turn.
   - After these turns, the bus is facing East when it reaches the school.

3. **Analyzing the Turns**:
   - **First Left Turn**: A left turn from the initial direction.
   - **Second Left Turn**: Another left turn from the new direction.
   - **Right Turn**: A right turn from the direction after the second left turn.

4. **Final Direction**: After these turns, the bus is facing East.

5. **Reverse Engineering the Initial Direction**:
   - If the bus is facing East after the sequence of turns, we can reverse the process to find the initial direction.
   - **Right Turn to East**: Before the right turn, the bus must have been facing South.
   - **Second Left Turn to South**: Before the second left turn, the bus must have been facing West.
   - **First Left Turn to West**: Before the first left turn, the bus must have been facing North.

6. **Conclusion**: Therefore, the bus was initially facing South at A's home.

**Explanation of Incorrect Options**:
- **Option 1 (North)**: If the bus was facing North initially, after two left turns and one right turn, it would not end up facing East.
- **Option 3 (East)**: If the bus was facing East initially, it would not require any turns to face East at the school, contradicting the sequence of turns.
- **Option 4 (West)**: If the bus was facing West initially, the sequence of turns would not result in the bus facing East at the school.

Thus, the correct answer is Option 2 (South), as it logically aligns with the given sequence of turns and the final direction of the bus.