Maykop and Belorechensk
Source: All-Russian 2007
May 4, 2007
combinatorics unsolvedcombinatorics
Problem Statement
The distance between Maykop and Belorechensk is km. Two of three friends need to reach Belorechensk from Maykop and another friend wants to reach Maykop from Belorechensk. They have only one bike, which is initially in Maykop. Each guy may go on foot (with velocity at most kmph) or on a bike (with velocity at most kmph). It is forbidden to leave a bike on a road. Prove that all of them may achieve their goals after hours minutes. (Only one guy may seat on the bike simultaneously).Folclore