"Chips Challenging Champions" by Schaeffer & Herik, has an article "Disjoint pattern database heuristics" by R.E. Korf and A. Felner, pp. 13-26. This is based on the Culberson/Schaeffer ideas of Computer Intelligence, v14.3 (1998) p 318-334. The Iterative-Deepening-A* algorithm is seen as necessary for the 15-puzzle. IDA* with the Manhatten Distance Function was the first algorithm to find optimal solutions to random instances of the 15-Puzzle. An average of 400m nodes are generated per problem instance in the search, requiring almost 5 hours of DEC 2060 time (as in 1984). Further ideas beyond IDA*/Manhatten are required for the 15- & 24-Puzzle. Their ideas reduce number of nodes by over 10,000 and running time by a factor of over 2,000. They averaged 2 days' computation (average) in solving 50 instances of the 24-Problem. With only the Manhatten_Distance concept, solving time would be 50,000 years per problem. Guy