MathDB
Game with a ball and n boxes

Source: Turkey JBMO Team Selection Test 2013, P3

May 31, 2013
geometrygeometric transformationcombinatorics proposedcombinatorics

Problem Statement

Two players AA and BB play a game with a ball and nn boxes placed onto the vertices of a regular nn-gon where nn is a positive integer. Initially, the ball is hidden in a box by player AA. At each step, BB chooses a box, then player AA says the distance of the ball to the selected box to player BB and moves the ball to an adjacent box. If BB finds the ball, then BB wins. Find the least number of steps for which BB can guarantee to win.