Why Some Puzzles Are Computationally Hard, Even for Computers
Why some puzzles are hard for computers: positions grow too fast to check, best answers are NP-hard, and clever estimates cannot remove the worst cases.
Riddle10 blog
Articles about sliding tile puzzle
How Computers Solve Puzzles: Search, Estimates and Logic
Computers solve puzzles by searching a network of positions. See breadth-first search, A*, greedy search and logic programs on one worked example.