slide puzzle

The original and still most common variety of this puzzle is the 15 puzzle. It consists of a plastic frame big enough to hold 16 small square pieces, and 15 such pieces are present, with the single hole allowing space to slide squares around. The target arrangement of the original puzzle by Sam Loyd was to start with the numbers in 1-15 order and end up with the same order but the 14 and 15 swapped. It turns out this is impossible to do without cheating.

The trick to such puzzles is to solve them one row or column at a time, until the last two rows which must be solved together. Also, the last two pieces of a row must be maneuvered alongside each other and put in place together. When you get down to the last two rows, each column consists of a "last two" type of move, where you need to maneuver the two pieces to be together and in the correct order, then rotate the whole bit to move them to the end where they belong.

There is a parity problem inherent in the 15 puzzle; any arrangement with exactly one pair of pieces swapped cannot be reached. Arrangements with an even number of pairs swapped can be reached. This is why Loyd's puzzle was unsolvable.

Sometimes these puzzles just have pieces numbered one to fifteen, but other versions sometimes use letters that spell out some short phrase. One classic version that has been used as a carnival game has one letter that repeats, once near the top and once near the bottom, and the carny intentionally mixes it up so that you're likely to put the wrong one at the top. Since the solution you'll be trying for has one pair of pieces switched, you'll never solve it unless you understand this trick.