Linda Skaring: Varianter av solitär

Abstract: The purpose of this thesis is to show that the fifth row is impossible to reach in the solitaire game Conway's Soldiers. The game was first analyzed in 1961 by John Horton Conway. The proof is based on the mathematical principle of invariance. The golden ratio also plays an important role in the argument, appearing in an unexpected way. By constructing a weighted function, it becomes possible to study how a certain value changes during the game and thereby prove that it can never increase in the manner required for the fifth row to be reached. The thesis also examines other variants of the game, including a version of Conway's Soldiers in which diagonal jumps are allowed, as well as the triangular version Pablito's Army. These examples demonstrate how small changes to the rules or the structure of the board can affect which positions or rows are possible to reach.