(A) study for the solvability of Fiver by a linear algebraic approach

Abstract

There is an interesting board game named Fiver. In this thesis, we prove that Fiver is always solvable in general width m, height n situation and find a polynomial-time algorithm giving a solution. Moreover, we investigate the reversibility of Fiver and also find a polynomial-time algorithm which determines whether it is reversible or not for given m, n. For a construction of algorithms and a proof of validity of algorithms, we use basic linear algebra facts in binary field. In our construction, we think imaginary width m, height infinity board. In addition, we investigate some properties of Fiver including inductive properties.