MathDB

33

Part of 1970 IMO Longlists

Problems(1)

Is this possible if we choose another P0 point?

Source: IMO LongList 1970 - P33

5/21/2011
The vertices of a given square are clockwise lettered A,B,C,DA,B,C,D. On the side ABAB is situated a point EE such that AE=AB/3AE = AB/3. Starting from an arbitrarily chosen point P0P_0 on segment AEAE and going clockwise around the perimeter of the square, a series of points P0,P1,P2,…P_0, P_1, P_2, \ldots is marked on the perimeter such that PiPi+1=AB/3P_iP_{i+1} = AB/3 for each ii. It will be clear that when P0P_0 is chosen in AA or in EE, then some PiP_i will coincide with P0P_0. Does this possibly also happen if P0P_0 is chosen otherwise?
geometryperimetercombinatorics unsolvedcombinatorics