There are two very strict laws in the country of Militaria.(i) Anyone who is shorter than 80% (or more) of his “neighbours” (i.e. men living at distance less then r from him) is freed from the military service.(ii) Anyone who is taller than 80% (or more) of his “neighbours” (i.e. men living at distance less then R from him) is allowed to serve in the police.A nice thing is that each man X may choose his own (possibly different) positive numbers r=r(X) and R=R(X). Can it happen that 90% (or more) of the men in Militaria are free from the army and, at the same time, 90% (or more) of the men in Militaria are allowed to serve in the police? (The places of living of the men are fixed points in the plane.)(N Konstantinov) combinatoricscombinatorial geometry