Square Pursuit Puzzle - Solution
The Puzzle:
Four people start at the corners of a square room, 10 meters on each side.
Each person moves at the same speed directly towards the next person counterclockwise as seen from above.
As a result, they spiral in until they all eventually collide at the center of the square. How far has each person traveled?
Our Solution:
If you stand still and someone moves continuously at right angles to the line between you, that person describes a circle around you. So their motion doesn't change the distance between you at all!
But in the pursuit problem, in each person's frame of reference, the target person is moving towards them.
So if the initial distance each person would have walked is 10 meters, then that's the distance they eventually walk to meet: just 10 meters.