Home > Riddles > The four tortugas
A curved chase that is resolved without describing the curve: it is enough to understand what distance is really being consumed.
Four turtles occupy the four corners of a square 10 centimeters on a side. They all start moving at the same time and at the same speed.
Each one always advances in the direction of the turtle in front of it, continually turning to aim at it. How far does each turtle travel before the four turtles meet?
By symmetry, the four turtles always continue to form the vertices of a square that shrinks as it rotates. Let's look at one turtle A and the next one, B.
A always moves directly toward B. The distance between them decreases at exactly the speed with which A moves in that direction, because B moves perpendicular to that instantaneous line of pursuit.
That means that the separation between A and B is reducing at the same speed with which A travels along the path. Since the initial distance between consecutive turtles is 10 cm, A will have traveled exactly 10 cm when that distance cancels out.
If you enjoyed this one, try more pure-logic riddles, explore this theme, browse the full archive, or read the riddle-solving guide.