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