## Class discussion

Physical Puzzles

We didn't have time to discuss the ins and outs of physical puzzles, but I include these notes for your reading pleasure:

From the Puzzle Museum (http://puzzlemuseum.com) comes a discussion and taxonomy of physical (or mechanical) puzzles: "A puzzle is a problem having one or more specific objectives, contrived for the principle purpose of exercising ones ingenuity and/or patience. A mechanical puzzle is a physical object comprising one or more parts which falls within the above definition... A puzzle should be classified by the problem that its designer intended the solver to encounter whilst attempting to solve it... A puzzle will be referred to as 2D if its third dimension is irrelevant (e.g. thickness of paper or plywood or an operation involving a third dimension such as folding). Most standard jigsaws are 2D; however jigsaws with sloping cuts in fact have a relevant third dimension, so they must be classed as 3D. The 14 main classes are as follows:

• DEXTERITY puzzles require the use of manual dexterity or other physical skills in their solution.
• ROUTEFINDING puzzles require the solver to find either any path, or a specific path as defined by certain rules.
• TANGLEMENT puzzles have parts that must be linked or unlinked. The linked parts, which may be flexible, have significant freedom of movement in relation to each other, unlike the parts of an interlocking puzzle.
• OPENING puzzles are puzzles in which the principle object is to open it, close it, undo it, remove something from it, or otherwise get it to work. They usually comprise a single object or associated parts such as a box with its lid, a padlock and its hasp, or a nut & bolt. The mechanism of the puzzle is not usually apparent, nor do they involve general assembly or disassembly of parts that interlock in 3D.
• INTERLOCKING puzzles interlock in three dimensions, i.e. one or more pieces hold the rest together, or the pieces are mutually self-sustaining.  Many clip-together puzzles are "non-interlocking".
• JIGSAW puzzles are made as if cut or stamped into pieces from a single complete object, and the principle objective is to restore them to their unique original form.
• ASSEMBLY puzzles require the arrangement of separate pieces to make specific shapes without regard to the sequence of that placing, they may clip together but do not interlock in 3D.  Some have a container and are posed as packing problems.
• PATTERN puzzles require the placing or arrangement of separate pieces of a similar nature to complete surface patterns according to defined rules. The pattern required may be the matching of edges of squares, faces of cubes, etc. The pattern may be color, texture, shape, etc. Where the pattern is due to differences in shape they must be sufficiently minor not to obscure the similarity of the pieces.
• FOLDING & HINGED puzzles have parts that are joined together and usually do not come apart. They are solved by hinging, flexing, or folding.
• SEQUENTIAL MOVEMENT puzzles are those that can be solved only by moves which can be seen to be dependant on previously made moves.
• JUGS & VESSELS have a mechanical puzzle or trick in their construction that affects the filling, pouring or drinking there from.
• OTHER TYPES OF MECHANICAL puzzles and objects are puzzle objects that do not easily fall into the above categories and cannot be categorized into sufficiently large groups to warrant their own major class. Included in this group are Balancing, Measuring, Cutting, Math, Logic, Trick, Mystery, & Theoretical puzzles. Also provision is made for puzzles pending classification.
• AMBIGUOUS PICTURES & PUZZLING OBJECTS in which something appears impossible or ambiguous.
• NON-PUZZLE but related EPHEMERA has been included as most puzzle collections include related ephemera which, whilst not strictly puzzles, need to be classified as part of the collection."
• Burr Puzzles

"A Burr puzzle consists of at least three rods intersecting each other at right angles. The most famous and well known type is the six piece burr where three sets of two rods intersect each other." From the IBM Burr Puzzle site.
A Burr puzzle is made from six intersecting pieces. Typically, each piece is 2×2×6 units in dimension, although there are many variations, including planar Burr puzzles, where the pices are 1×4×6 (See Vreugd's Burr). I've been experimenting with 2×3×4 puzzles (See Walter's Burr). The parts of the piece that protrude from the center are the same for every piece. The interesting thing is what happens in the interior regions of the puzzle.
There are three classes of 2×2×6 Burr puzzles: (1) puzzles with a solid (key) piece; (2) puzzles that slide apart--typically into hemispheres; and (3) puzzles that unlock with one or more slides.

I've modeled in Lego four puzzles featured on the IBM site:

You can make your own puzzles using Lego. (In building with Lego, the key is: two bricks wide = five plates high.) You can make a unit cube by using a standard 2×2 brick and adding a plate and flat plate. Thus, to make a Burr-puzzle piece, you should start with a 2×12 brick and expand from there. I find that using the 1×12 bricks with holes to add stability to my Burrs.