Application of Fundamental Group To Hanging Puzzle

Author: Edet, S.A
Department of Mathematics,  University of Ibadan, Ibadan.

 

On May 1997, A. Spivak posed a puzzle he called the Hanging Puzzle. The generalized form of this puzzle goes thus; given a string and a frame, how can one loop the string around n-nails such that, the removal of any k-subsets of n-nails would fall the picture hanging on the string. The purpose of this paper is to solve the simple generalization of the puzzle (1-out-of- n) from the algebraic topological perspective. We use the van Kampen’s theorem to reduce the topological problem to an algebra one. Hence we solve the problem by providing an algebraic solution.