Inspector Simon Mart looked at the old sign on the door of his office with his name: Inspector Mart, S. That his parents had bestowed just one initial on him, had been one of his life long irritations. He probably should have told his parents before his birth that he wanted many birth names. But perhaps he could persuade the guys who provided the signs on the doors that his initial should precede his family name, and not come after it. Well, he had his own room and that was a benefit that should last until the next reorganization.
His manager had dumped a file on his desk. He read the attached note: ‘to be solved last month’. It was the 29th of the month, and he decided that this urgency would allow him to start with a mug of coffee and a social chat with his fellow inspectors at he coffee machine. At the coffee machine he met a new and pretty police officer and he chatted for a quarter of an hour with her. After that chat he decided to pick up this file. It contained a number of reports as well as a copy of interrogations. He summoned that a couple of matchsticks encrusted with amethysts had been stolen from the London Matchbox Museum. There were three suspects, Jim, Jack and John, all well known criminals. It was known that none of them could speak two consecutive true statements. He looked at the interrogation reports:
Jim: Jack did it. John is innocent.
Jack: John did it. Jim is innocent.
John: Jim is innocent. Jack is innocent.
In the train I overheard calling a woman her friend: “I saw five blouses, but I had only money enough for four of them. I could have bought four of them for 65,80, or a combination of four of them for 61,80, or four others for 58,80, or another combination for 57,80, or still another combination for 54,80. But I was just 5 cents short of buying all of them. How much money did she have with her?
I tried the app and the puzzles start out easy, but soon turn out to present decent challenges. Reason enough for a post on this type of puzzles. I’ll limit myself in this post to 2d sliding block puzzles. There are many 3d sliding block puzzles too: puzzle collectors may remember the many secret boxes puzzles, often beautifully crafted by woodworkers. But those are worth a different post.
There are many types of sliding block puzzles. Sam Loyds 15 puzzle is probably the most famous one. Many sliding block puzzles have been computerized, and the Sokoban puzzles are perhaps the first type of sliding block puzzle that exists only as a computer puzzle and not as a mechanical puzzle. But in this post I’d like to take a closer look at the type of sliding block puzzle that at the English wikipedia is called Klotski. I feel some doubt at this name: it may be derived from polish, as the article says, but when I view the history of the article I think it is more likely that Klotski is the name of a computer or video game instead of the name of this type of puzzle. I have never encountered the name Klotski for this type of puzzle in any puzzle book.
Sliding Piece Puzzles (by Edward Hordern, 1986, Oxford University Press, ISBN 0-19-853204-0) is said to be the definitive volume on this type of puzzle. It lists 270 of his sliding block puzzles, all neatly categorized and with the solution in the shortest number of moves. That brings us of course to the question: what is a move?
Hordern lists 4 possibilities:
a) a sliding block is moved as many ‘units’ in one or more directions
b) a sliding block is moved one ‘unit’ in 1 direction
c) a group of sliding blocks is moved one or more units in 1 direction.
d) a sliding block is moved one or more units in one direction.
Option a) is most common among puzzlers, mainly because it corresponds with a physical action: move a block as far as you want without lifting your finger from the piece.
Horderns also subdivides sliding block puzzles in four categories:
I. Sliding block pieces – pieces move independent of each other.
II. Warehouse/soko puzzles: one piece pushes others.
III. Railway shunting puzzles – one or two pieces push or pull all the others
IV. Puzzles with plungers or levers.
I already treated railway shunting puzzles, and category IV is a group of rather rare and complicated puzzles. This post deals entirely with group I, and with the subgroup where pieces are rectangular and of unequal size.
The nice thing about mechanical puzzles is that you can patent them, such as USA patent 207,124.
I’m not sure about the early history of sliding block puzzles. Sam Loyds puzzles goes back to the 1870’s. One Henry Walton filed U.S. Patent 516,035 on 1893-03-14 for a sliding puzzle resembling 15-puzzle. According to Edward Hordern, this is the first even known sliding puzzle with rectangular blocks.
Horderns book “sliding block puzzles”, mentioned above, is the standard work of reference for this type of puzzle.
Sam and Moshe start to explore a cave. They both have a torch and both torches start with the same length. Sam’s torch will burn 3 hours while Moshe’s torch will burn 4 hours. When they get out, they find that one torch has exactly three times as many centimeters left as the other.