“…Six positions required exactly 80 moves, 4 of them have previously been detected by Gasser [12]. The new ones are (15,14,13,12,10,11,8,9,2,6,5,1,3,7,4,0) and (15,11,13,12,14,10,9,5,2,6,8,1,3,7,4,0). The computation proves that the hardest 15-puzzle positions require exactly 80 moves to be solved.…”