Question

A, B, C and D are standing on the four corners of a square field as shown in the figure. From the positions shown in the figure, A walks to North position and B walks to the East position while C decides to walk two sides in anticlockwise direction. B walks to North and then changes his mind to take the previous position. Identify the choice with correct positions.

• A. A & B occupy the same position.
• B. C & D occupy the same position.
• C. D & B are in their original positions.
• D. B & C are diagonally opposite positions.

Hint:

Move each person one edge at a time along the square, starting from A, then B, then C two sides anticlockwise, and remember D never moves.

Answer 1

The Correct Option is D

A cleaner way to solve this kind of position tracking question is to name the four corners by compass direction first, north west, north east, south east and south west, and then simply update one label at a time as each person moves, instead of trying to picture all the moves happening together.

Starting layout: A is at south west, B is at north west, C is at north east, D is at south east, with north pointing to the top of the page.

1. A walks to North: from south west, moving toward north along the same side of the square lands A at north west. A's new spot: north west.
2. B walks to East: from north west, moving toward east along the top side of the square lands B at north east. B's new spot: north east.
3. C walks two sides anticlockwise: going around the square anticlockwise means the order of corners is north west, south west, south east, north east, and back to north west. Starting at north east and taking two steps in this anticlockwise order lands C first at north west, then at south west. C's new spot: south west.
4. D does not move: the question never mentions D taking any action, so D remains at south east throughout.
5. B's extra detour: the sentence about B walking to North and then changing his mind to take the previous position simply means B thought about moving further north from his new spot, but backed out and returned to the position he was already holding, which is north east. This does not change B's final spot.

Final layout: A at north west, B at north east, C at south west, D at south east.

Now check each option against this final layout:

• A and B occupy the same position: false, A is north west and B is north east, different corners.
• C and D occupy the same position: false, C is south west and D is south east, different corners.
• D and B are in their original positions: false, D is indeed still at its original south east corner, but B has moved away from its original north west corner to north east, so this option fails on B.
• B and C are diagonally opposite positions: true, B is at north east and C is at south west, and on a square, north east and south west are the two ends of one diagonal, so they are diagonally opposite.

The correct answer is option (4), B and C are diagonally opposite positions.