13th Iberoamerican 1998

P₁, P₂, ... , P_n are points in the plane and r₁, r₂, ... , r_n are real numbers such that the distance between P_i and P_j is r_i + r_j (for i not equal to j). Find the largest n for which this is possible.

Solution

Answer: n = 4.

Draw a circle radius r_i at P_i. Then each pair of circles must touch. But that is possible iff n ≤ 4.

13th Ibero 1998

© John Scholes
jscholes@kalva.demon.co.uk
24 Oct 2002