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