Problem #PRU-78680

Problemas Geometría Geometría plana Círculos Ángulo central. Longitud de arco y circunferencia Métodos Inducción matemática Inducción matemática en geometría Principio de casillas Principio de casillas (número finito de puntos, líneas, etc.)

Problem

On a circle of radius 1, the point \(O\) is marked and from this point, to the right, a notch is marked using a compass of radius \(l\). From the obtained notch \(O_1\), a new notch is marked, in the same direction with the same radius and this is process is repeated 1968 times. After this, the circle is cut at all 1968 notches, and we get 1968 arcs. How many different lengths of arcs can this result in?