COMPLETE SOLUTION OF THE'EIGHT-PUZZLE' P. D. A. SCHOFIELD

'For the last few weeks, the "Fifteen-puzzle" has been prominently before the American Public, and may safely be said to have engaged the attention of nine out of ten persons of both sexes and of all ages and conditions of the community.' The Tight-puzzle' is a reduced form of the'Fifteen-puzzle', the subject of the somewhat extravagant claim quoted above. Its use in the study of learning processes, both human and programmed, is described in two other papers in this volume, Michie (p. This paper describes the calculation of optimum solutions to all the 20 160 possible versions of the puzzle. The'Eight-puzzle' consists of eight square pieces, numbered 0-7,f capable of sliding in a shallow square tray of size nine times that of the individual pieces: there is thus one empty square.