Here are some examples of reasoning questions on direction sense:

Example 1: Simple Direction Sense

Question:
A person walks 10 meters towards the north, turns right, and walks 5 meters. Then, he turns left and walks 10 meters. In which direction is he now from his original position?

Solution:

• The person starts at the origin.
• He walks 10 meters north.
• He turns right (which is east) and walks 5 meters.
• Then, he turns left (which is north) and walks 10 meters.

He is now facing east and is 5 meters east of his original position.

Example 2: Multiple Turns

Question:
A man walks 20 meters towards the east, then turns left and walks 30 meters. He turns right and walks 20 meters. After that, he turns left again and walks 10 meters. Where is he now in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 20 meters east.
3. Turns left (north) and walks 30 meters.
4. Turns right (east) and walks 20 meters.
5. Turns left (north) and walks 10 meters.

He is now 30 meters north and 40 meters east of his starting point.

Example 3: Opposite Directions

Question:
A person walks 10 meters north, then 5 meters south. After that, he turns to his right and walks 5 meters. In which direction is he now from his starting point?

Solution:

• The person starts at the origin.
• He walks 10 meters north.
• Then, he walks 5 meters south, which places him 5 meters north of the starting point.
• He turns right (which is west) and walks 5 meters.

So, he is now 5 meters north and 5 meters west of his starting point.

Example 4: Square Path

Question:
A person walks 10 meters towards the north, turns left, and walks 10 meters. Then, he turns left again and walks 10 meters. Finally, he turns left one more time and walks 10 meters. Where is he now?

Solution:

• Starts at the origin.
• Walks 10 meters north.
• Turns left (west) and walks 10 meters.
• Turns left again (south) and walks 10 meters.
• Turns left again (east) and walks 10 meters.

He is now back at his starting point.

Example 5: Direction Calculation with Landmarks

Question:
A man walks 30 meters towards the north. He then turns to his right and walks 20 meters. After turning left, he walks 30 meters and then turns left again and walks 20 meters. How far is he from his original position, and in which direction?

Solution:

1. Starts at the origin.
2. Walks 30 meters north.
3. Turns right (east) and walks 20 meters.
4. Turns left (north) and walks 30 meters.
5. Turns left again (west) and walks 20 meters.

He is now back at his starting point (same position). Therefore, he is 0 meters from his original position.

Example 6: Complex Path with Multiple Turns

Question:
A man walks 15 meters towards the east, then turns left and walks 10 meters. After that, he turns left again and walks 5 meters. Finally, he turns left again and walks 10 meters. In which direction is he from his starting point?

Solution:

1. Starts at the origin.
2. Walks 15 meters east.
3. Turns left (north) and walks 10 meters.
4. Turns left again (west) and walks 5 meters.
5. Turns left again (south) and walks 10 meters.

He is now 10 meters south of his starting point.

Example 7: Right Turns and Final Direction

Question:
A person walks 40 meters towards the north, turns right and walks 20 meters, turns right again and walks 40 meters, and finally turns right and walks 20 meters. In which direction is he now from his starting position?

Solution:

1. Starts at the origin.
2. Walks 40 meters north.
3. Turns right (east) and walks 20 meters.
4. Turns right again (south) and walks 40 meters.
5. Turns right again (west) and walks 20 meters.

He is now back at his starting point (same position).

Example 8: Reverse Turns

Question:
A man walks 20 meters towards the west, then turns to his left and walks 20 meters. After that, he turns left again and walks 10 meters. Finally, he turns right and walks 5 meters. In which direction is he from his starting point?

Solution:

1. Starts at the origin.
2. Walks 20 meters west.
3. Turns left (south) and walks 20 meters.
4. Turns left again (east) and walks 10 meters.
5. Turns right (south) and walks 5 meters.

He is now 25 meters south and 10 meters west of his starting point.

Example 9: Opposite Path Calculation

Question:
A person starts at point A, walks 15 meters towards the north, turns right and walks 10 meters, then turns right and walks 15 meters, and turns right again to walk 10 meters. Where is he in relation to his starting point?

Solution:

1. Starts at point A (origin).
2. Walks 15 meters north.
3. Turns right (east) and walks 10 meters.
4. Turns right again (south) and walks 15 meters.
5. Turns right again (west) and walks 10 meters.

He is back at his starting point, so he is at point A (same position).

Example 10: Multiple Left Turns

Question:
A man walks 50 meters towards the south, turns left and walks 20 meters, turns left again and walks 50 meters, and finally turns left and walks 20 meters. Where is he now in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 50 meters south.
3. Turns left (east) and walks 20 meters.
4. Turns left again (north) and walks 50 meters.
5. Turns left again (west) and walks 20 meters.

He is now back at his starting point (same position).

Example 11: Reverse Directions

Question:
A person walks 30 meters north, turns right and walks 20 meters, then turns left and walks 30 meters. Finally, he turns left and walks 20 meters. Where is he now in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 30 meters north.
3. Turns right (east) and walks 20 meters.
4. Turns left (north) and walks 30 meters.
5. Turns left (west) and walks 20 meters.

He is back at his starting point.

Example 12: Mixed Directions and Return

Question:
A person walks 25 meters towards the east, turns left and walks 35 meters, turns right and walks 25 meters, and finally turns right again and walks 35 meters. Where is he now?

Solution:

1. Starts at the origin.
2. Walks 25 meters east.
3. Turns left (north) and walks 35 meters.
4. Turns right (east) and walks 25 meters.
5. Turns right again (south) and walks 35 meters.

He is back at his starting point, so he is at the origin.

Example 13: Complex Multiple Turns

Question:
A man walks 50 meters to the north, turns left and walks 30 meters, then turns left again and walks 50 meters, and finally turns right and walks 20 meters. What is his position relative to his starting point?

Solution:

1. Starts at the origin.
2. Walks 50 meters north.
3. Turns left (west) and walks 30 meters.
4. Turns left again (south) and walks 50 meters.
5. Turns right (west) and walks 20 meters.

He is now 30 meters west of his original position and 20 meters south.

Example 14: Path with Diagonal Turns

Question:
A person starts at point P. He walks 30 meters north, turns right, walks 20 meters, turns right again and walks 30 meters. Finally, he turns left and walks 20 meters. Where is he now in relation to point P?

Solution:

1. Starts at point P (origin).
2. Walks 30 meters north.
3. Turns right (east) and walks 20 meters.
4. Turns right again (south) and walks 30 meters.
5. Turns left (east) and walks 20 meters.

He is back at point P (same position), so he’s at the origin.

Example 15: Circular Path

Question:
A man walks 10 meters east, turns left and walks 10 meters, turns left and walks 10 meters, and turns left again and walks 10 meters. What is his final position in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 10 meters east.
3. Turns left (north) and walks 10 meters.
4. Turns left again (west) and walks 10 meters.
5. Turns left again (south) and walks 10 meters.

He is back at his starting point (same position), so he is at the origin.

Example 16: Three Right Turns

Question:
A person walks 20 meters towards the north, turns right and walks 30 meters, then turns right and walks 20 meters. Finally, he turns right again and walks 30 meters. Where is he now in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 20 meters north.
3. Turns right (east) and walks 30 meters.
4. Turns right again (south) and walks 20 meters.
5. Turns right again (west) and walks 30 meters.

He is back at his starting point (same position), so he is at the origin.

Example 17: Starting in Different Directions

Question:
A man walks 40 meters towards the south, turns left and walks 50 meters, then turns left again and walks 40 meters, and turns left and walks 50 meters. Where is he now?

Solution:

1. Starts at the origin.
2. Walks 40 meters south.
3. Turns left (east) and walks 50 meters.
4. Turns left again (north) and walks 40 meters.
5. Turns left again (west) and walks 50 meters.

He is back at his starting point (same position), so he is at the origin.

Example 18: Compound Path

Question:
A person starts at point A. He walks 15 meters north, turns left and walks 25 meters, turns right and walks 15 meters, and turns right again and walks 25 meters. Where is he now in relation to point A?

Solution:

1. Starts at point A.
2. Walks 15 meters north.
3. Turns left (west) and walks 25 meters.
4. Turns right (north) and walks 15 meters.
5. Turns right again (east) and walks 25 meters.

He is back at point A (same position), so he is at the origin.

Example 19: Multiple Left Turns and Distances

Question:
A person starts at point X. He walks 60 meters towards the north, turns left and walks 40 meters, turns left again and walks 60 meters, and turns left once more and walks 40 meters. Where is he in relation to point X?

Solution:

1. Starts at point X.
2. Walks 60 meters north.
3. Turns left (west) and walks 40 meters.
4. Turns left again (south) and walks 60 meters.
5. Turns left again (east) and walks 40 meters.

He is back at point X (same position), so he is at the origin.

Example 20: Path with Two Right Turns

Question:
A person walks 50 meters towards the west, turns right and walks 20 meters, turns right again and walks 50 meters. Where is he in relation to his starting position?

Solution:

1. Starts at the origin.
2. Walks 50 meters west.
3. Turns right (north) and walks 20 meters.
4. Turns right again (east) and walks 50 meters.

He is now 20 meters north of his starting point.

Example 21: North-South Movement

Question:
A man walks 30 meters north, turns right and walks 40 meters, turns left and walks 30 meters, then turns left and walks 40 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 30 meters north.
3. Turns right (east) and walks 40 meters.
4. Turns left (north) and walks 30 meters.
5. Turns left again (west) and walks 40 meters.

He is back at his starting point (same position), so he is at the origin.

Example 22: Mixed Directions with Offsets

Question:
A person starts at point A and walks 25 meters towards the north. He then turns left and walks 15 meters, turns left again and walks 25 meters, and finally turns left and walks 15 meters. Where is he in relation to point A?

Solution:

1. Starts at point A.
2. Walks 25 meters north.
3. Turns left (west) and walks 15 meters.
4. Turns left again (south) and walks 25 meters.
5. Turns left again (east) and walks 15 meters.

He is back at point A (same position), so he is at the origin.

Example 23: Right and Left Turns in a Square

Question:
A person walks 20 meters towards the north, turns right and walks 20 meters, turns right again and walks 20 meters, and turns right again and walks 20 meters. Where is he now in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 20 meters north.
3. Turns right (east) and walks 20 meters.
4. Turns right again (south) and walks 20 meters.
5. Turns right again (west) and walks 20 meters.

He is back at his starting point (same position), so he is at the origin.

Example 24: Multiple Right Turns in a Circle

Question:
A man walks 15 meters towards the east, then turns right and walks 10 meters. After that, he turns right again and walks 15 meters. Finally, he turns right again and walks 10 meters. Where is he now in relation to his starting position?

Solution:

1. Starts at the origin.
2. Walks 15 meters east.
3. Turns right (south) and walks 10 meters.
4. Turns right again (west) and walks 15 meters.
5. Turns right again (north) and walks 10 meters.

He is back at his starting point (same position), so he is at the origin.

Example 25: Complex Multiple Turns with Distances

Question:
A man walks 40 meters to the north, turns left and walks 30 meters, turns left and walks 40 meters, and turns left and walks 30 meters. Where is he now in relation to his starting position?

Solution:

1. Starts at the origin.
2. Walks 40 meters north.
3. Turns left (west) and walks 30 meters.
4. Turns left again (south) and walks 40 meters.
5. Turns left again (east) and walks 30 meters.

He is back at his starting point (same position), so he is at the origin.

Example 26: Moving in Different Directions

Question:
A person walks 10 meters towards the north, then turns to his right and walks 20 meters. After that, he turns left and walks 10 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 10 meters north.
3. Turns right (east) and walks 20 meters.
4. Turns left (north) and walks 10 meters.

He is now 20 meters east of his starting point.

Example 27: Reaching the Same Point

Question:
A person walks 50 meters to the south, then turns left and walks 30 meters. He turns left again and walks 50 meters, and finally turns left and walks 30 meters. Where is he now in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 50 meters south.
3. Turns left (east) and walks 30 meters.
4. Turns left again (north) and walks 50 meters.
5. Turns left again (west) and walks 30 meters.

He is back at his starting point (same position), so he is at the origin.

Example 28: Path with Multiple Left Turns

Question:
A person walks 20 meters towards the west, turns left and walks 20 meters, turns left again and walks 20 meters, and turns left once more and walks 20 meters. Where is he now?

Solution:

1. Starts at the origin.
2. Walks 20 meters west.
3. Turns left (south) and walks 20 meters.
4. Turns left again (east) and walks 20 meters.
5. Turns left again (north) and walks 20 meters.

He is back at his starting point (same position), so he is at the origin.

Example 29: Moving in a Zigzag Pattern

Question:
A man walks 10 meters towards the north, turns right and walks 15 meters, turns right and walks 10 meters, turns left and walks 15 meters. Where is he now in relation to his starting position?

Solution:

1. Starts at the origin.
2. Walks 10 meters north.
3. Turns right (east) and walks 15 meters.
4. Turns right again (south) and walks 10 meters.
5. Turns left (east) and walks 15 meters.

He is now 15 meters east of his starting point.

Example 30: Combining Distances and Turns

Question:
A man walks 60 meters to the east, turns left and walks 40 meters, turns left again and walks 60 meters, and turns left one more time and walks 40 meters. What is his final position in relation to the starting point?

Solution:

1. Starts at the origin.
2. Walks 60 meters east.
3. Turns left (north) and walks 40 meters.
4. Turns left again (west) and walks 60 meters.
5. Turns left again (south) and walks 40 meters.

He is back at the starting point (same position), so he is at the origin.

Example 31: Moving in a Rectangular Path

Question:
A person walks 30 meters north, then turns right and walks 50 meters. After that, he turns right again and walks 30 meters. Finally, he turns right again and walks 50 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 30 meters north.
3. Turns right (east) and walks 50 meters.
4. Turns right again (south) and walks 30 meters.
5. Turns right again (west) and walks 50 meters.

He is back at the starting point (same position), so he is at the origin.

Example 32: Direction after Complex Turns

Question:
A man walks 20 meters north, turns left and walks 10 meters, turns left and walks 20 meters, and turns right and walks 10 meters. In which direction is he now from his starting point?

Solution:

1. Starts at the origin.
2. Walks 20 meters north.
3. Turns left (west) and walks 10 meters.
4. Turns left again (south) and walks 20 meters.
5. Turns right (west) and walks 10 meters.

He is now 20 meters south and 10 meters west of his starting point.

Example 33: Multiple Right and Left Turns

Question:
A person walks 30 meters towards the east, then turns right and walks 40 meters, turns right again and walks 30 meters, and finally turns right again and walks 40 meters. Where is he now in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 30 meters east.
3. Turns right (south) and walks 40 meters.
4. Turns right again (west) and walks 30 meters.
5. Turns right again (north) and walks 40 meters.

He is back at his starting point (same position), so he is at the origin.

Example 34: Multiple Turns with Distinct Distances

Question:
A man walks 20 meters north, then turns left and walks 25 meters, turns left again and walks 20 meters, and turns right and walks 25 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 20 meters north.
3. Turns left (west) and walks 25 meters.
4. Turns left again (south) and walks 20 meters.
5. Turns right (west) and walks 25 meters.

He is back at his starting point (same position), so he is at the origin.

Example 35: A Square Path with Distances

Question:
A person walks 40 meters south, turns left and walks 40 meters, turns left again and walks 40 meters, and turns left and walks 40 meters. Where is he now in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 40 meters south.
3. Turns left (east) and walks 40 meters.
4. Turns left again (north) and walks 40 meters.
5. Turns left again (west) and walks 40 meters.

He is back at his starting point (same position), so he is at the origin.

Example 36: North, South, East, and West Movement

Question:
A man walks 50 meters north, turns left and walks 50 meters, turns left again and walks 50 meters, and turns left again and walks 50 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 50 meters north.
3. Turns left (west) and walks 50 meters.
4. Turns left again (south) and walks 50 meters.
5. Turns left again (east) and walks 50 meters.

He is back at his starting point (same position), so he is at the origin.

Example 37: Complex Path with Several Turns

Question:
A person walks 60 meters north, turns left and walks 30 meters, turns left again and walks 60 meters, and turns left and walks 30 meters. What is his final position in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 60 meters north.
3. Turns left (west) and walks 30 meters.
4. Turns left again (south) and walks 60 meters.
5. Turns left again (east) and walks 30 meters.

He is back at his starting point (same position), so he is at the origin.

Example 38: Path with Turns in Different Directions

Question:
A person walks 25 meters south, turns right and walks 35 meters, turns left and walks 25 meters, then turns right and walks 35 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 25 meters south.
3. Turns right (west) and walks 35 meters.
4. Turns left (south) and walks 25 meters.
5. Turns right (west) and walks 35 meters.

He is back at his starting point (same position), so he is at the origin.

Example 39: Diagonal Turns and Distances

Question:
A man walks 40 meters to the north, turns left and walks 40 meters, turns left and walks 30 meters, and finally turns left and walks 30 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 40 meters north.
3. Turns left (west) and walks 40 meters.
4. Turns left again (south) and walks 30 meters.
5. Turns left again (east) and walks 30 meters.

He is now 10 meters north of his starting point.

Example 40: Backtracking Path

Question:
A person walks 25 meters towards the north, turns left and walks 10 meters, turns right and walks 25 meters, and turns right again and walks 10 meters. What is his final position in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 25 meters north.
3. Turns left (west) and walks 10 meters.
4. Turns right (north) and walks 25 meters.
5. Turns right again (east) and walks 10 meters.

He is back at his starting point (same position), so he is at the origin.

Example 41: Complex Path with Diagonal Movement

Question:
A person walks 30 meters south, turns right and walks 20 meters, turns left and walks 30 meters, then turns left and walks 20 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 30 meters south.
3. Turns right (west) and walks 20 meters.
4. Turns left (south) and walks 30 meters.
5. Turns left again (east) and walks 20 meters.

He is back at his starting point (same position), so he is at the origin.

Example 42: Circular Movement

Question:
A person walks 50 meters to the north, turns right and walks 50 meters, turns right again and walks 50 meters, and finally turns right again and walks 50 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 50 meters north.
3. Turns right (east) and walks 50 meters.
4. Turns right again (south) and walks 50 meters.
5. Turns right again (west) and walks 50 meters.

He is back at his starting point (same position), so he is at the origin.

Example 43: Repeated Turns with Equal Distances

Question:
A man walks 25 meters to the north, then turns right and walks 25 meters, turns right again and walks 25 meters, and finally turns right and walks 25 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 25 meters north.
3. Turns right (east) and walks 25 meters.
4. Turns right again (south) and walks 25 meters.
5. Turns right again (west) and walks 25 meters.

He is back at his starting point (same position), so he is at the origin.

Example 44: Path with Diagonal and Straight Turns

Question:
A man walks 30 meters to the north, turns right and walks 40 meters, turns right again and walks 30 meters, and turns left and walks 40 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 30 meters north.
3. Turns right (east) and walks 40 meters.
4. Turns right again (south) and walks 30 meters.
5. Turns left (east) and walks 40 meters.

He is back at his starting point (same position), so he is at the origin.

Example 45: Path with Unmatched Distances

Question:
A person walks 40 meters south, then turns left and walks 50 meters, then turns left again and walks 40 meters, and turns left again and walks 30 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 40 meters south.
3. Turns left (east) and walks 50 meters.
4. Turns left again (north) and walks 40 meters.
5. Turns left again (west) and walks 30 meters.

He is 10 meters east of his starting point.

Example 46: Moving Along the Edges

Question:
A person starts at point A, walks 20 meters north, turns left and walks 20 meters, turns left and walks 30 meters, then turns left and walks 20 meters. Where is he in relation to point A?

Solution:

1. Starts at point A.
2. Walks 20 meters north.
3. Turns left (west) and walks 20 meters.
4. Turns left again (south) and walks 30 meters.
5. Turns left again (east) and walks 20 meters.

He is 10 meters south of point A.

Example 47: Multiple Right Turns with Same Distances

Question:
A person walks 60 meters north, turns right and walks 60 meters, turns right again and walks 60 meters, and turns right one more time and walks 60 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 60 meters north.
3. Turns right (east) and walks 60 meters.
4. Turns right again (south) and walks 60 meters.
5. Turns right again (west) and walks 60 meters.

He is back at his starting point (same position), so he is at the origin.

Example 48: Uneven Movements in Multiple Directions

Question:
A person walks 100 meters to the north, turns left and walks 50 meters, turns left again and walks 100 meters, then turns left and walks 50 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 100 meters north.
3. Turns left (west) and walks 50 meters.
4. Turns left again (south) and walks 100 meters.
5. Turns left again (east) and walks 50 meters.

He is back at his starting point (same position), so he is at the origin.

Example 49: Complex Path Involving All Four Directions

Question:
A person walks 30 meters north, turns left and walks 40 meters, turns left again and walks 30 meters, and turns left once more and walks 40 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 30 meters north.
3. Turns left (west) and walks 40 meters.
4. Turns left again (south) and walks 30 meters.
5. Turns left again (east) and walks 40 meters.

He is back at his starting point (same position), so he is at the origin.

Example 50: Circular Movement with Turns

Question:
A person walks 40 meters north, turns right and walks 50 meters, turns right and walks 40 meters, and turns right and walks 50 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 40 meters north.
3. Turns right (east) and walks 50 meters.
4. Turns right again (south) and walks 40 meters.
5. Turns right again (west) and walks 50 meters.

He is back at his starting point (same position), so he is at the origin.

Example 51: Walking in a Rectangular Path

Question:
A man walks 30 meters east, turns left and walks 50 meters, turns left and walks 30 meters, and turns left again and walks 50 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 30 meters east.
3. Turns left (north) and walks 50 meters.
4. Turns left again (west) and walks 30 meters.
5. Turns left again (south) and walks 50 meters.

He is back at his starting point (same position), so he is at the origin.

Example 52: Back and Forth Path with Distinct Turns

Question:
A person walks 70 meters north, turns right and walks 30 meters, turns right and walks 70 meters, then turns right and walks 30 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 70 meters north.
3. Turns right (east) and walks 30 meters.
4. Turns right again (south) and walks 70 meters.
5. Turns right again (west) and walks 30 meters.

He is back at his starting point (same position), so he is at the origin.

Example 53: Path with Rectangular Turns

Question:
A person walks 50 meters to the north, then turns left and walks 30 meters, turns left again and walks 50 meters, and turns left again and walks 30 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 50 meters north.
3. Turns left (west) and walks 30 meters.
4. Turns left again (south) and walks 50 meters.
5. Turns left again (east) and walks 30 meters.

He is back at his starting point (same position), so he is at the origin.

Example 54: Multiple Right Turns

Question:
A person walks 80 meters to the south, turns right and walks 60 meters, turns right again and walks 80 meters, and turns right once more and walks 60 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 80 meters south.
3. Turns right (west) and walks 60 meters.
4. Turns right again (north) and walks 80 meters.
5. Turns right again (east) and walks 60 meters.

He is back at his starting point (same position), so he is at the origin.

Example 55: Path with Equal and Unequal Distances

Question:
A person walks 40 meters to the west, turns left and walks 60 meters, turns left and walks 40 meters, and turns left and walks 70 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 40 meters west.
3. Turns left (south) and walks 60 meters.
4. Turns left again (east) and walks 40 meters.
5. Turns left again (north) and walks 70 meters.

He is now 30 meters north of his starting point.

Example 56: Circular Path with Equal Turns

Question:
A person walks 50 meters to the north, turns right and walks 50 meters, turns right again and walks 50 meters, and turns right one more time and walks 50 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 50 meters north.
3. Turns right (east) and walks 50 meters.
4. Turns right again (south) and walks 50 meters.
5. Turns right again (west) and walks 50 meters.

He is back at his starting point (same position), so he is at the origin.

Example 57: Complex Right and Left Turns

Question:
A man walks 100 meters east, turns left and walks 50 meters, turns left again and walks 100 meters, and turns left again and walks 50 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 100 meters east.
3. Turns left (north) and walks 50 meters.
4. Turns left again (west) and walks 100 meters.
5. Turns left again (south) and walks 50 meters.

He is back at his starting point (same position), so he is at the origin.

Example 58: Movement in Multiple Directions

Question:
A person walks 25 meters north, turns right and walks 35 meters, turns left and walks 25 meters, turns left again and walks 35 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 25 meters north.
3. Turns right (east) and walks 35 meters.
4. Turns left (north) and walks 25 meters.
5. Turns left again (west) and walks 35 meters.

He is back at his starting point (same position), so he is at the origin.

Example 59: Path Forming a Square

Question:
A person walks 20 meters to the south, turns right and walks 20 meters, turns right again and walks 20 meters, and turns right again and walks 20 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 20 meters south.
3. Turns right (west) and walks 20 meters.
4. Turns right again (north) and walks 20 meters.
5. Turns right again (east) and walks 20 meters.

He is back at his starting point (same position), so he is at the origin.

Example 60: Path with Multiple Left Turns

Question:
A person walks 60 meters north, turns left and walks 40 meters, turns left again and walks 60 meters, and turns left once more and walks 40 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 60 meters north.
3. Turns left (west) and walks 40 meters.
4. Turns left again (south) and walks 60 meters.
5. Turns left again (east) and walks 40 meters.

He is back at his starting point (same position), so he is at the origin.

Example 61: Unequal Distances and Multiple Turns

Question:
A person walks 50 meters to the north, turns right and walks 30 meters, turns right and walks 50 meters, and turns right again and walks 20 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 50 meters north.
3. Turns right (east) and walks 30 meters.
4. Turns right again (south) and walks 50 meters.
5. Turns right again (west) and walks 20 meters.

He is now 10 meters east of his starting point.

Example 62: Mixed Movements with Different Turns

Question:
A man walks 20 meters to the east, turns left and walks 20 meters, turns left again and walks 30 meters, and turns left again and walks 40 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 20 meters east.
3. Turns left (north) and walks 20 meters.
4. Turns left again (west) and walks 30 meters.
5. Turns left again (south) and walks 40 meters.

He is 10 meters south of his starting point.

Example 63: Movement in All Directions

Question:
A person walks 60 meters north, turns right and walks 40 meters, turns left and walks 60 meters, turns left again and walks 40 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 60 meters north.
3. Turns right (east) and walks 40 meters.
4. Turns left (north) and walks 60 meters.
5. Turns left again (west) and walks 40 meters.

He is back at his starting point (same position), so he is at the origin.

Example 64: Path with Square-like Movements

Question:
A person walks 50 meters to the north, turns right and walks 50 meters, turns right again and walks 50 meters, and turns right again and walks 50 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 50 meters north.
3. Turns right (east) and walks 50 meters.
4. Turns right again (south) and walks 50 meters.
5. Turns right again (west) and walks 50 meters.

He is back at his starting point (same position), so he is at the origin.

Also read: Reasoning question on sitting arrangement

Example 65: Complex Path with Uneven Distances

Question:
A person walks 70 meters to the north, turns left and walks 50 meters, turns left and walks 70 meters, and turns left and walks 40 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 70 meters north.
3. Turns left (west) and walks 50 meters.
4. Turns left again (south) and walks 70 meters.
5. Turns left again (east) and walks 40 meters.

He is now 10 meters west of his starting point.

Example 66: Same Distance with Different Directions

Question:
A person walks 40 meters north, turns right and walks 40 meters, turns right again and walks 40 meters, and turns right again and walks 40 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 40 meters north.
3. Turns right (east) and walks 40 meters.
4. Turns right again (south) and walks 40 meters.
5. Turns right again (west) and walks 40 meters.

He is back at his starting point (same position), so he is at the origin.

Example 67: Movements in Different Directions

Question:
A person walks 60 meters south, turns left and walks 40 meters, turns left and walks 60 meters, and turns left and walks 50 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 60 meters south.
3. Turns left (east) and walks 40 meters.
4. Turns left again (north) and walks 60 meters.
5. Turns left again (west) and walks 50 meters.

He is now 10 meters west of his starting point.

Example 68: Square Path with Multiple Turns

Question:
A person walks 90 meters east, turns left and walks 90 meters, turns left again and walks 90 meters, and turns left again and walks 90 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 90 meters east.
3. Turns left (north) and walks 90 meters.
4. Turns left again (west) and walks 90 meters.
5. Turns left again (south) and walks 90 meters.

He is back at his starting point (same position), so he is at the origin.

Example 69: Path with Long Movements

Question:
A person walks 150 meters to the north, turns left and walks 100 meters, turns left again and walks 150 meters, and turns left once more and walks 100 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 150 meters north.
3. Turns left (west) and walks 100 meters.
4. Turns left again (south) and walks 150 meters.
5. Turns left again (east) and walks 100 meters.

He is back at his starting point (same position), so he is at the origin.

Example 70: Rectangular Movement with Unequal Distances

Question:
A person walks 120 meters north, turns left and walks 80 meters, turns left again and walks 120 meters, and turns left again and walks 100 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 120 meters north.
3. Turns left (west) and walks 80 meters.
4. Turns left again (south) and walks 120 meters.
5. Turns left again (east) and walks 100 meters.

He is now 20 meters west of his starting point.

Example 71: Path with Four Turns

Question:
A person walks 100 meters east, turns left and walks 50 meters, turns left and walks 100 meters, and turns left and walks 50 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 100 meters east.
3. Turns left (north) and walks 50 meters.
4. Turns left again (west) and walks 100 meters.
5. Turns left again (south) and walks 50 meters.

He is back at his starting point (same position), so he is at the origin.

Example 72: L-Shaped Path with Uneven Distances

Question:
A person walks 100 meters to the west, turns left and walks 50 meters, turns left again and walks 100 meters, and turns left again and walks 30 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 100 meters west.
3. Turns left (south) and walks 50 meters.
4. Turns left again (east) and walks 100 meters.
5. Turns left again (north) and walks 30 meters.

He is now 20 meters south of his starting point.

Example 73: Large Square Movement

Question:
A person walks 200 meters north, turns left and walks 200 meters, turns left and walks 200 meters, and turns left and walks 200 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 200 meters north.
3. Turns left (west) and walks 200 meters.
4. Turns left again (south) and walks 200 meters.
5. Turns left again (east) and walks 200 meters.

He is back at his starting point (same position), so he is at the origin.

Example 74: Right and Left Turns with Equal Distances

Question:
A person walks 60 meters north, turns right and walks 60 meters, turns left and walks 60 meters, and turns left again and walks 60 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 60 meters north.
3. Turns right (east) and walks 60 meters.
4. Turns left (north) and walks 60 meters.
5. Turns left again (west) and walks 60 meters.

He is back at his starting point (same position), so he is at the origin.

Example 75: Walk with Complex Directions

Question:
A person walks 40 meters to the south, turns left and walks 30 meters, turns right and walks 40 meters, turns right and walks 30 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 40 meters south.
3. Turns left (east) and walks 30 meters.
4. Turns right (south) and walks 40 meters.
5. Turns right again (west) and walks 30 meters.

He is back at his starting point (same position), so he is at the origin.

Example 76: Rectangular Movement with Equal Distances

Question:
A person walks 40 meters north, turns right and walks 40 meters, turns right again and walks 40 meters, and turns right again and walks 40 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 40 meters north.
3. Turns right (east) and walks 40 meters.
4. Turns right again (south) and walks 40 meters.
5. Turns right again (west) and walks 40 meters.

He is back at his starting point (same position), so he is at the origin.

Example 77: Uneven Distances with Four Turns

Question:
A person walks 100 meters north, turns left and walks 60 meters, turns left again and walks 100 meters, and turns left again and walks 80 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 100 meters north.
3. Turns left (west) and walks 60 meters.
4. Turns left again (south) and walks 100 meters.
5. Turns left again (east) and walks 80 meters.

He is now 20 meters east of his starting point.

Example 78: Circular Path with Equal Turns

Question:
A person walks 50 meters to the north, turns right and walks 50 meters, turns right again and walks 50 meters, and turns right again and walks 50 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 50 meters north.
3. Turns right (east) and walks 50 meters.
4. Turns right again (south) and walks 50 meters.
5. Turns right again (west) and walks 50 meters.

He is back at his starting point (same position), so he is at the origin.

Example 79: Long Distance with Multiple Turns

Question:
A person walks 200 meters east, turns left and walks 150 meters, turns left again and walks 200 meters, and turns left and walks 100 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 200 meters east.
3. Turns left (north) and walks 150 meters.
4. Turns left again (west) and walks 200 meters.
5. Turns left again (south) and walks 100 meters.

He is now 50 meters north of his starting point.

Example 80: Small Square Movement

Question:
A person walks 10 meters north, turns left and walks 10 meters, turns left again and walks 10 meters, and turns left again and walks 10 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 10 meters north.
3. Turns left (west) and walks 10 meters.
4. Turns left again (south) and walks 10 meters.
5. Turns left again (east) and walks 10 meters.

He is back at his starting point (same position), so he is at the origin.

Example 81: Unequal Movement with Multiple Left Turns

Question:
A person walks 30 meters east, turns left and walks 20 meters, turns left again and walks 30 meters, and turns left again and walks 40 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 30 meters east.
3. Turns left (north) and walks 20 meters.
4. Turns left again (west) and walks 30 meters.
5. Turns left again (south) and walks 40 meters.

He is now 20 meters south of his starting point.

Example 82: Path Making a Rectangle

Question:
A person walks 80 meters north, turns left and walks 50 meters, turns left again and walks 80 meters, and turns left again and walks 50 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 80 meters north.
3. Turns left (west) and walks 50 meters.
4. Turns left again (south) and walks 80 meters.
5. Turns left again (east) and walks 50 meters.

He is back at his starting point (same position), so he is at the origin.

Example 83: Path with Long Movement and Right Turns

Question:
A person walks 120 meters to the east, turns right and walks 80 meters, turns right again and walks 120 meters, and turns right again and walks 50 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 120 meters east.
3. Turns right (south) and walks 80 meters.
4. Turns right again (west) and walks 120 meters.
5. Turns right again (north) and walks 50 meters.

He is now 30 meters south of his starting point.

Example 84: Multiple Turns in One Direction

Question:
A person walks 60 meters north, turns right and walks 60 meters, turns right and walks 60 meters, turns right and walks 60 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 60 meters north.
3. Turns right (east) and walks 60 meters.
4. Turns right again (south) and walks 60 meters.
5. Turns right again (west) and walks 60 meters.

He is back at his starting point (same position), so he is at the origin.

Example 85: Uneven Movement with Different Distances

Question:
A person walks 40 meters north, turns right and walks 50 meters, turns left and walks 40 meters, and turns left and walks 50 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 40 meters north.
3. Turns right (east) and walks 50 meters.
4. Turns left (north) and walks 40 meters.
5. Turns left (west) and walks 50 meters.

He is back at his starting point (same position), so he is at the origin.

Example 86: Path with Multiple Right and Left Turns

Question:
A person walks 100 meters north, turns left and walks 100 meters, turns right and walks 50 meters, and turns left and walks 100 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 100 meters north.
3. Turns left (west) and walks 100 meters.
4. Turns right (north) and walks 50 meters.
5. Turns left (west) and walks 100 meters.

He is now 50 meters west of his starting point.

Example 87: Large Movement with Four Turns

Question:
A person walks 300 meters south, turns left and walks 200 meters, turns left again and walks 300 meters, and turns left again and walks 200 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 300 meters south.
3. Turns left (east) and walks 200 meters.
4. Turns left again (north) and walks 300 meters.
5. Turns left again (west) and walks 200 meters.

He is back at his starting point (same position), so he is at the origin.

Example 88: Square Path with Different Distances

Question:
A person walks 40 meters south, turns left and walks 60 meters, turns left again and walks 40 meters, and turns left again and walks 60 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 40 meters south.
3. Turns left (east) and walks 60 meters.
4. Turns left again (north) and walks 40 meters.
5. Turns left again (west) and walks 60 meters.

He is back at his starting point (same position), so he is at the origin.

Example 89: L-Shaped Movement

Question:
A person walks 100 meters to the east, turns left and walks 200 meters, turns left again and walks 100 meters, and turns left again and walks 300 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 100 meters east.
3. Turns left (north) and walks 200 meters.
4. Turns left again (west) and walks 100 meters.
5. Turns left again (south) and walks 300 meters.

He is now 100 meters south of his starting point.

Example 90: Equal Distance Walks

Question:
A person walks 150 meters north, turns left and walks 150 meters, turns left again and walks 150 meters, and turns left again and walks 150 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 150 meters north.
3. Turns left (west) and walks 150 meters.
4. Turns left again (south) and walks 150 meters.
5. Turns left again (east) and walks 150 meters.

He is back at his starting point (same position), so he is at the origin.

Example 91: Uneven Distances with Four Turns

Question:
A person walks 80 meters to the south, turns right and walks 100 meters, turns right again and walks 80 meters, and turns right again and walks 50 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 80 meters south.
3. Turns right (west) and walks 100 meters.
4. Turns right again (north) and walks 80 meters.
5. Turns right again (east) and walks 50 meters.

He is now 50 meters west of his starting point.

Example 92: Equal Turns with Long Movements

Question:
A person walks 300 meters to the east, turns left and walks 300 meters, turns left again and walks 300 meters, and turns left again and walks 300 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 300 meters east.
3. Turns left (north) and walks 300 meters.
4. Turns left again (west) and walks 300 meters.
5. Turns left again (south) and walks 300 meters.

He is back at his starting point (same position), so he is at the origin.

Example 93: Moving in Four Directions

Question:
A person walks 150 meters to the north, turns left and walks 100 meters, turns left again and walks 150 meters, and turns left again and walks 50 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 150 meters north.
3. Turns left (west) and walks 100 meters.
4. Turns left again (south) and walks 150 meters.
5. Turns left again (east) and walks 50 meters.

He is now 50 meters west of his starting point.

Example 94: Path with Longer Movements

Question:
A person walks 200 meters to the west, turns right and walks 400 meters, turns right again and walks 200 meters, and turns right again and walks 400 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 200 meters west.
3. Turns right (north) and walks 400 meters.
4. Turns right again (east) and walks 200 meters.
5. Turns right again (south) and walks 400 meters.

He is back at his starting point (same position), so he is at the origin.

Example 95: Path with Left and Right Turns

Question:
A person walks 50 meters to the east, turns left and walks 100 meters, turns left again and walks 50 meters, and turns left again and walks 200 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 50 meters east.
3. Turns left (north) and walks 100 meters.
4. Turns left again (west) and walks 50 meters.
5. Turns left again (south) and walks 200 meters.

He is now 150 meters south of his starting point.

Example 96: Square-like Movement with Uneven Distances

Question:
A person walks 120 meters to the north, turns right and walks 80 meters, turns right again and walks 120 meters, and turns right again and walks 60 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 120 meters north.
3. Turns right (east) and walks 80 meters.
4. Turns right again (south) and walks 120 meters.
5. Turns right again (west) and walks 60 meters.

He is now 20 meters east of his starting point.

Example 97: Path with Multiple Left Turns

Question:
A person walks 70 meters to the north, turns left and walks 30 meters, turns left again and walks 70 meters, and turns left again and walks 30 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 70 meters north.
3. Turns left (west) and walks 30 meters.
4. Turns left again (south) and walks 70 meters.
5. Turns left again (east) and walks 30 meters.

He is back at his starting point (same position), so he is at the origin.

Example 98: Uneven Movements with Turns

Question:
A person walks 120 meters south, turns left and walks 150 meters, turns left again and walks 120 meters, and turns left again and walks 200 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 120 meters south.
3. Turns left (east) and walks 150 meters.
4. Turns left again (north) and walks 120 meters.
5. Turns left again (west) and walks 200 meters.

He is now 50 meters west of his starting point.

Example 99: Moving in All Four Directions

Question:
A person walks 80 meters north, turns right and walks 50 meters, turns left and walks 80 meters, and turns left again and walks 100 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 80 meters north.
3. Turns right (east) and walks 50 meters.
4. Turns left (north) and walks 80 meters.
5. Turns left again (west) and walks 100 meters.

He is now 50 meters west of his starting point.

Example 100: Long Movements with Right Turns

Question:
A person walks 150 meters to the south, turns right and walks 200 meters, turns right again and walks 150 meters, and turns right again and walks 200 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 150 meters south.
3. Turns right (west) and walks 200 meters.
4. Turns right again (north) and walks 150 meters.
5. Turns right again (east) and walks 200 meters.

He is back at his starting point (same position), so he is at the origin.

Example 101: Diagonal Path with Turns

Question:
A person walks 120 meters north, turns right and walks 100 meters, turns right again and walks 120 meters, and turns right again and walks 100 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 120 meters north.
3. Turns right (east) and walks 100 meters.
4. Turns right again (south) and walks 120 meters.
5. Turns right again (west) and walks 100 meters.

He is back at his starting point (same position), so he is at the origin.

Example 102: Longer East-West Path

Question:
A person walks 150 meters to the north, turns left and walks 200 meters, turns left again and walks 150 meters, and turns left again and walks 300 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 150 meters north.
3. Turns left (west) and walks 200 meters.
4. Turns left again (south) and walks 150 meters.
5. Turns left again (east) and walks 300 meters.

He is now 100 meters east of his starting point.

Example 103: Large Rectangular Movement

Question:
A person walks 200 meters to the east, turns right and walks 100 meters, turns right again and walks 200 meters, and turns right again and walks 100 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 200 meters east.
3. Turns right (south) and walks 100 meters.
4. Turns right again (west) and walks 200 meters.
5. Turns right again (north) and walks 100 meters.

He is back at his starting point (same position), so he is at the origin.

Example 104: Uneven Movements with Large Turns

Question:
A person walks 300 meters to the north, turns left and walks 400 meters, turns left again and walks 300 meters, and turns left again and walks 100 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 300 meters north.
3. Turns left (west) and walks 400 meters.
4. Turns left again (south) and walks 300 meters.
5. Turns left again (east) and walks 100 meters.

He is now 300 meters west of his starting point.

Example 105: Path with Longer Turns

Question:
A person walks 400 meters to the west, turns left and walks 300 meters, turns left again and walks 400 meters, and turns left again and walks 300 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 400 meters west.
3. Turns left (south) and walks 300 meters.
4. Turns left again (east) and walks 400 meters.
5. Turns left again (north) and walks 300 meters.

He is back at his starting point (same position), so he is at the origin.

Example 106: Moving with Different Turn Sizes

Question:
A person walks 120 meters to the north, turns right and walks 150 meters, turns right again and walks 120 meters, and turns right again and walks 100 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 120 meters north.
3. Turns right (east) and walks 150 meters.
4. Turns right again (south) and walks 120 meters.
5. Turns right again (west) and walks 100 meters.

He is now 50 meters east of his starting point.

Example 107: Movement with Long Path and Three Turns

Question:
A person walks 300 meters to the east, turns left and walks 300 meters, turns left again and walks 400 meters, and turns left again and walks 200 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 300 meters east.
3. Turns left (north) and walks 300 meters.
4. Turns left again (west) and walks 400 meters.
5. Turns left again (south) and walks 200 meters.

He is now 100 meters west of his starting point.

Example 108: Unequal Movements with Left Turns

Question:
A person walks 250 meters to the north, turns left and walks 150 meters, turns left again and walks 250 meters, and turns left again and walks 100 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 250 meters north.
3. Turns left (west) and walks 150 meters.
4. Turns left again (south) and walks 250 meters.
5. Turns left again (east) and walks 100 meters.

He is now 50 meters west of his starting point.

Example 109: Square Path with Multiple Left Turns

Question:
A person walks 100 meters to the north, turns left and walks 100 meters, turns left again and walks 100 meters, and turns left again and walks 100 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 100 meters north.
3. Turns left (west) and walks 100 meters.
4. Turns left again (south) and walks 100 meters.
5. Turns left again (east) and walks 100 meters.

He is back at his starting point (same position), so he is at the origin.

Example 110: Multiple Right Turns

Question:
A person walks 50 meters to the east, turns right and walks 100 meters, turns right again and walks 50 meters, and turns right again and walks 200 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 50 meters east.
3. Turns right (south) and walks 100 meters.
4. Turns right again (west) and walks 50 meters.
5. Turns right again (north) and walks 200 meters.

He is now 100 meters north of his starting point.

Example 111: Large Movement with Small Turns

Question:
A person walks 300 meters south, turns left and walks 50 meters, turns left again and walks 300 meters, and turns left again and walks 50 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 300 meters south.
3. Turns left (east) and walks 50 meters.
4. Turns left again (north) and walks 300 meters.
5. Turns left again (west) and walks 50 meters.

He is back at his starting point (same position), so he is at the origin.

Example 112: Large Square Path

Question:
A person walks 500 meters to the east, turns right and walks 500 meters, turns right again and walks 500 meters, and turns right again and walks 500 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 500 meters east.
3. Turns right (south) and walks 500 meters.
4. Turns right again (west) and walks 500 meters.
5. Turns right again (north) and walks 500 meters.

He is back at his starting point (same position), so he is at the origin.

Example 113: Path with Left and Right Turns

Question:
A person walks 250 meters to the north, turns right and walks 150 meters, turns left and walks 250 meters, and turns left again and walks 100 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 250 meters north.
3. Turns right (east) and walks 150 meters.
4. Turns left (north) and walks 250 meters.
5. Turns left again (west) and walks 100 meters.

He is now 50 meters west of his starting point.

Example 114: Square Path with Large Steps

Question:
A person walks 400 meters to the east, turns right and walks 400 meters, turns right again and walks 400 meters, and turns right again and walks 400 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 400 meters east.
3. Turns right (south) and walks 400 meters.
4. Turns right again (west) and walks 400 meters.
5. Turns right again (north) and walks 400 meters.

He is back at his starting point (same position), so he is at the origin.

Example 115: Uneven Turns

Question:
A person walks 200 meters north, turns left and walks 300 meters, turns left again and walks 200 meters, and turns left again and walks 400 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 200 meters north.
3. Turns left (west) and walks 300 meters.
4. Turns left again (south) and walks 200 meters.
5. Turns left again (east) and walks 400 meters.

He is now 100 meters east of his starting point.

Example 116: Path with Larger Moves

Question:
A person walks 500 meters to the west, turns right and walks 700 meters, turns right again and walks 500 meters, and turns right again and walks 700 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 500 meters west.
3. Turns right (north) and walks 700 meters.
4. Turns right again (east) and walks 500 meters.
5. Turns right again (south) and walks 700 meters.

He is back at his starting point (same position), so he is at the origin.

Example 117: Turning Right and Left with Different Lengths

Question:
A person walks 250 meters to the east, turns left and walks 150 meters, turns left again and walks 250 meters, and turns left again and walks 100 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 250 meters east.
3. Turns left (north) and walks 150 meters.
4. Turns left again (west) and walks 250 meters.
5. Turns left again (south) and walks 100 meters.

He is now 150 meters south of his starting point.

Example 118: Unequal Movements and Turns

Question:
A person walks 100 meters south, turns left and walks 150 meters, turns left again and walks 100 meters, and turns left again and walks 200 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 100 meters south.
3. Turns left (east) and walks 150 meters.
4. Turns left again (north) and walks 100 meters.
5. Turns left again (west) and walks 200 meters.

He is now 50 meters west of his starting point.

Example 119: Repeated Turn Pattern

Question:
A person walks 100 meters to the north, turns left and walks 100 meters, turns left again and walks 100 meters, and turns left again and walks 100 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 100 meters north.
3. Turns left (west) and walks 100 meters.
4. Turns left again (south) and walks 100 meters.
5. Turns left again (east) and walks 100 meters.

He is back at his starting point (same position), so he is at the origin.

Example 120: Long Distance with Turns

Question:
A person walks 200 meters to the north, turns left and walks 400 meters, turns left again and walks 200 meters, and turns left again and walks 600 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 200 meters north.
3. Turns left (west) and walks 400 meters.
4. Turns left again (south) and walks 200 meters.
5. Turns left again (east) and walks 600 meters.

He is now 400 meters east of his starting point.

Example 121: Square with Longer Side Movements

Question:
A person walks 500 meters to the north, turns left and walks 700 meters, turns left again and walks 500 meters, and turns left again and walks 700 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 500 meters north.
3. Turns left (west) and walks 700 meters.
4. Turns left again (south) and walks 500 meters.
5. Turns left again (east) and walks 700 meters.

He is back at his starting point (same position), so he is at the origin.

Example 122: Path with Multiple Turns

Question:
A person walks 150 meters to the south, turns right and walks 250 meters, turns right again and walks 150 meters, and turns right again and walks 300 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 150 meters south.
3. Turns right (west) and walks 250 meters.
4. Turns right again (north) and walks 150 meters.
5. Turns right again (east) and walks 300 meters.

He is now 50 meters east of his starting point.

Example 123: Path with Equal Turns and Longer Distance

Question:
A person walks 600 meters to the north, turns right and walks 400 meters, turns right again and walks 600 meters, and turns right again and walks 400 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 600 meters north.
3. Turns right (east) and walks 400 meters.
4. Turns right again (south) and walks 600 meters.
5. Turns right again (west) and walks 400 meters.

He is back at his starting point (same position), so he is at the origin.

Example 124: Path with Unequal Right and Left Turns

Question:
A person walks 150 meters to the east, turns left and walks 200 meters, turns left again and walks 150 meters, and turns left again and walks 50 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 150 meters east.
3. Turns left (north) and walks 200 meters.
4. Turns left again (west) and walks 150 meters.
5. Turns left again (south) and walks 50 meters.

He is now 150 meters south of his starting point.

Example 125: Path with Diagonal Turn Pattern

Question:
A person walks 200 meters to the north, turns left and walks 300 meters, turns left again and walks 200 meters, and turns left again and walks 400 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 200 meters north.
3. Turns left (west) and walks 300 meters.
4. Turns left again (south) and walks 200 meters.
5. Turns left again (east) and walks 400 meters.

He is now 100 meters east of his starting point.

Example 126: Path with Unequal Distances

Question:
A person walks 400 meters to the north, turns left and walks 300 meters, turns left again and walks 400 meters, and turns left again and walks 200 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 400 meters north.
3. Turns left (west) and walks 300 meters.
4. Turns left again (south) and walks 400 meters.
5. Turns left again (east) and walks 200 meters.

He is now 100 meters west of his starting point.

Example 127: Short Movements with Multiple Turns

Question:
A person walks 100 meters to the south, turns left and walks 50 meters, turns left again and walks 100 meters, and turns left again and walks 50 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 100 meters south.
3. Turns left (east) and walks 50 meters.
4. Turns left again (north) and walks 100 meters.
5. Turns left again (west) and walks 50 meters.

He is back at his starting point (same position), so he is at the origin.

Example 128: Large Rectangular Movement

Question:
A person walks 300 meters to the east, turns right and walks 500 meters, turns right again and walks 300 meters, and turns right again and walks 500 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 300 meters east.
3. Turns right (south) and walks 500 meters.
4. Turns right again (west) and walks 300 meters.
5. Turns right again (north) and walks 500 meters.

He is back at his starting point (same position), so he is at the origin.

Example 129: Smaller Path with Multiple Left Turns

Question:
A person walks 100 meters to the east, turns left and walks 150 meters, turns left again and walks 100 meters, and turns left again and walks 50 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 100 meters east.
3. Turns left (north) and walks 150 meters.
4. Turns left again (west) and walks 100 meters.
5. Turns left again (south) and walks 50 meters.

He is now 100 meters north of his starting point.

Example 130: Circular Path with Right Turns

Question:
A person walks 200 meters to the north, turns right and walks 200 meters, turns right again and walks 200 meters, and turns right again and walks 200 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 200 meters north.
3. Turns right (east) and walks 200 meters.
4. Turns right again (south) and walks 200 meters.
5. Turns right again (west) and walks 200 meters.

He is back at his starting point (same position), so he is at the origin.

Example 131: Complex Path with Unequal Turns

Question:
A person walks 150 meters to the north, turns right and walks 100 meters, turns right again and walks 150 meters, and turns left and walks 100 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 150 meters north.
3. Turns right (east) and walks 100 meters.
4. Turns right again (south) and walks 150 meters.
5. Turns left (east) and walks 100 meters.

He is 100 meters east of his starting point.

Example 132: Diagonal Movement with Multiple Right Turns

Question:
A person walks 200 meters to the north, turns right and walks 300 meters, turns right again and walks 200 meters, and turns right again and walks 100 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 200 meters north.
3. Turns right (east) and walks 300 meters.
4. Turns right again (south) and walks 200 meters.
5. Turns right again (west) and walks 100 meters.

He is now 200 meters east of his starting point.

Example 133: Square Path with Large Steps

Question:
A person walks 400 meters to the east, turns right and walks 400 meters, turns right again and walks 400 meters, and turns right again and walks 400 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 400 meters east.
3. Turns right (south) and walks 400 meters.
4. Turns right again (west) and walks 400 meters.
5. Turns right again (north) and walks 400 meters.

He is back at his starting point (same position), so he is at the origin.

Example 134: Unequal Square Path

Question:
A person walks 300 meters to the north, turns left and walks 400 meters, turns left again and walks 300 meters, and turns left again and walks 200 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 300 meters north.
3. Turns left (west) and walks 400 meters.
4. Turns left again (south) and walks 300 meters.
5. Turns left again (east) and walks 200 meters.

He is now 200 meters west of his starting point.

Example 135: More Complex Path with Multiple Right and Left Turns

Question:
A person walks 150 meters to the east, turns left and walks 300 meters, turns left again and walks 150 meters, turns right and walks 200 meters, turns right again and walks 150 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 150 meters east.
3. Turns left (north) and walks 300 meters.
4. Turns left again (west) and walks 150 meters.
5. Turns right (north) and walks 200 meters.
6. Turns right again (east) and walks 150 meters.

He is now 200 meters north of his starting point.

Example 136: Large Distance with Circular Turns

Question:
A person walks 500 meters to the south, turns right and walks 300 meters, turns right again and walks 500 meters, and turns right again and walks 300 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 500 meters south.
3. Turns right (west) and walks 300 meters.
4. Turns right again (north) and walks 500 meters.
5. Turns right again (east) and walks 300 meters.

He is back at his starting point (same position), so he is at the origin.

Example 137: Path with Unequal Distances and Turns

Question:
A person walks 600 meters to the west, turns left and walks 200 meters, turns left again and walks 600 meters, and turns left again and walks 100 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 600 meters west.
3. Turns left (south) and walks 200 meters.
4. Turns left again (east) and walks 600 meters.
5. Turns left again (north) and walks 100 meters.

He is now 100 meters south of his starting point.

Example 138: Circular Path with Complex Turns

Question:
A person walks 700 meters to the east, turns right and walks 500 meters, turns right again and walks 700 meters, and turns right again and walks 500 meters. Where is he in relation to his starting point?

Solution:

1. Starts at the origin.
2. Walks 700 meters east.
3. Turns right (south) and walks 500 meters.
4. Turns right again (west) and walks 700 meters.
5. Turns right again (north) and walks 500 meters.

He is back at his starting point (same position), so he is at the origin.

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