To solve this problem, let us analyze Max's movements step by step:

1. Initial Information:

   • Max turned 2 right angles in the anti-clockwise direction and then 3 right angles in the clockwise direction.
   • He ended up facing the fire station.

2. Anti-clockwise Movement:

   • Each right angle is $90^\circ$.
   • Turning 2 right angles anti-clockwise means $2 \times 90^\circ = 180^\circ$. This is a half-circle turn in the anti-clockwise direction.

3. Clockwise Movement:

   • Turning 3 right angles clockwise means $3 \times 90^\circ = 270^\circ$. This is a three-quarter-circle turn in the clockwise direction.

4. Net Movement:

   • First, Max turns 180° anti-clockwise.
   • Then, he turns 270° clockwise. The net movement is: $270^\circ (\text{clockwise}) - 180^\circ (\text{anti-clockwise}) = 90^\circ (\text{clockwise}).$
   • A 90° clockwise turn places Max at a location to his immediate right.

5. End Position:

   • Max ends up facing the fire station. From the diagram, if he makes a 90° clockwise turn from his starting direction, he ends up at the fire station.

6. Original Direction:

   • To determine the original direction, we reverse the final 90° clockwise movement. Facing the fire station and turning 90° anti-clockwise places Max at the grocery store.

Answer: Max was initially facing the grocery store.

Would you like me to clarify any steps further or explain another approach?

Related Questions:

1. How do clockwise and anti-clockwise directions differ geometrically?
2. How would the solution change if Max turned 4 right angles instead of 3 clockwise?
3. What happens to the net direction if Max turns equal angles clockwise and anti-clockwise?
4. How do you calculate the total angle for multiple turns in mixed directions?
5. Can you apply this logic to a compass (N, E, S, W)?

Tip:

Always track directions by labeling angles relative to a starting point or using cardinal directions for reference.