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(094) 2

Part of 1985 Tournament Of Towns

Problems(1)

TOT 094 1985 Spring S2 radius of a circle rotates at a speed

Source:

8/24/2019
The radius OMOM of a circle rotates uniformly at a rate of 360/n360/n degrees per second , where nn is a positive integer . The initial radius is OM0OM_0. After 11 second the radius is OM1OM_1 , after two more seconds (i.e. after three seconds altogether) the radius is OM2OM_2 , after 33 more seconds (after 66 seconds altogether) the radius is OM3OM_3, ..., after n−1n - 1 more seconds its position is OMn−1OM_{n-1}. For which values of nn do the points M0,M1,...,Mn−1M_0, M_1 , ..., M_{n-1} divide the circle into nn equal arcs? (a) Is it true that the powers of 22 are such values? (b) Does there exist such a value which is not a power of 22?
(V. V. Proizvolov , Moscow)
rotationradiusspeedarccirclecombinatorial geometrygeometry