Puzzle Making for Woodworkers Donald Bell SFW Meeting
Puzzle Making for Woodworkers Donald Bell SFW Meeting, January 2011 Email : donald@marchland. org Web site : www. bellwoodwork. com
Puzzle Making for Woodworkers What makes a good puzzle? - It should be easy to describe - Fairly easy to make (either one or many) - Not trivial to solve, but not dauntingly difficult either (solving time between 10 and 30 minutes, perhaps) - The “look and feel” should be attractive - There should be a surprise – either an “Aha!” factor or several puzzles in one
Puzzle Making for Woodworkers The puzzle-maker’s progress - Solving other people’s puzzles Copying other people’s puzzles Modifying other people’s puzzles Creating original puzzles of your own Developing the manufacturing processes Documentation, packaging, sharing …
Different kinds of puzzle illustrated here - put-together puzzles (2 D) - put-together puzzles (3 D) - "steady hand" puzzles - sequential puzzles Also (but not shown here) - take-apart puzzles - (especially "burr" puzzles) - scroll-saw puzzles - sliding block puzzles - secret compartment boxes
More kinds of puzzle illustrated here (back cover of same book) - put-together puzzles - "steady hand" puzzles - sequential puzzles Also (not really puzzles) - magic tricks - games of skill
The “Blockhead” Puzzle - Easy to describe Not hard to make Not trivial to solve Definitely an “Aha!” moment when you work out how to do it
A Brief Tour of the Workshop Band Saw Record Power BS 350 1½ HP cut depth 230 mm, throat 340 mm
Woodturning Lathe Record Power, Model CL 3 ¾ HP, 5 -speed belt drive
Table Saw Record Power TS 200 SB 2 HP, 4000 rpm 250 mm (10") blade Sliding Beam (605 mm travel)
Sliding Beam, Mitre Fence, 45 degree tilt
Disk Sander Clarke CDS 300 mm diameter 1 HP, 1450 rpm
Radial Arm Drill Press Axminster AWBRD 550 ¾ HP, 5 speed belt drive
Portable Router Clarke Contractor CR 2 3 HP, 21000 rpm ½" collet
The Puzzle Maker's Toolkit
A few puzzles for you to play with – this is a secret opening box (there is something under that thumb!)
A well-known, easy to make puzzle The "Soma" Cube Four small cubes can be put together in eight different ways, including a straight stick and a square. The other six pieces, plus a 3 -cube L-shape, make up the Soma Cube Puzzle. Easy to make and not too hard to solve. There are 240 solutions Alternatively, take away the L-shape piece and use the other six pieces to make a big L-shape twice the size. A bit harder.
A puzzle with an "Aha!" factor Conways's Curious Cube Six of the pieces are 2" x 1" blocks. And there are three 1" x 1" cubes. They can be assembled into a 3" x 3" cube, but there is only one way of doing it. (John Horton Conway is a mathematician who has produced many wonderful puzzles)
The Fifth Chair Puzzle The four chairs are the same shape, but different sizes. Two small, one medium, one large. Use them all to make a fifth (giant) chair, the same shape as the others. Height Width Depth Can you ALSO discover the mathematical principle that makes the puzzle possible? Small 63. 0 50. 0 39. 7 Medium 79. 4 63. 0 50. 0 Here are the dimensions of the chairs in mm. Large 100. 0 79. 4 63. 0 Giant 126. 0 100. 0 79. 4
Easy to Make, Very Hard to Solve Professor Hoffman's Cube 27 identical blocks of wood (often made in 27 different types of wood) If they were all perfect cubes, 5 x 5 x 5, they could easily be packed into a 15 x 15 cube. But these are 4 x 5 x 6, so each one can have one of six orientations. A 4 x 5 x 6 block has 4% less volume than a 5 x 5 x 5 cube, so there a few small gaps in each layer Here are three layers of one solution, but it is hard to find
Another "Aha!" puzzle “Blockhead” Bill Cutler won the Grand Prize at the 1986 Hikimi Wooden Puzzle Competition. Four blocks in a box - Tip them out and then try to put them back! - It’s harder than it looks This one can be made on the table saw without the use of jigs
The “Blockhead” Puzzle - The four blocks are not quite cubical - Square on the top - One side vertical - Two sides sloping OUT at 5 degrees - One side sloping IN at 10 degrees
The “Blockhead” Puzzle The sides of the box are undercut by 5 degrees The box opening is 81 mm square (to accommodate the 40 mm blocks)
The “Blockhead” Puzzle The sides of the box are undercut by 5 degrees, then mitred at 45 degrees for the corners. A 6 mm plywood base to finish
The “Blockhead” Puzzle The stock for the blocks is 40 mm thick, then cut at 5 degree and 10 degree angles, giving a width of 40 mm on the top Some trial cuts may be needed to get the 40 mm width just right
“Blockhead” Puzzle The "stick" is clamped to the sliding beam, the mitre gauge is set to 0 degrees for the first cut (maybe trimming the wood after the previous block) The stick is advanced to meet the guide block (fixed to the rip-fence with double sided tape) The mitre gauge is set to 5 degrees for the second cut Then the process is repeated. Note that there is a danger of getting both "right handed" and "left handed" blocks (the puzzle would then be impossible!)
A puzzle that needs a complex jig Nob's "never-ending" puzzle (Nob Yoshigahara – famous puzzle maker) A cube, sliced in half by an oblique plane
Nob's never-ending puzzle The two half-cubes can be glued together in an L-shape, 16 different ways
Nob's never-ending puzzle Eight of the possible 16 pieces form "Nob's Never-Ending Puzzle"
Nob's never-ending puzzle They can be assembled into many interesting shapes (with some difficulty)
Nob's never-ending puzzle Actually only 11 shapes can be made (and some need to be supported)
Nob's puzzle – making the pieces Making a small cube (just 40 mm on a side) and then slicing it across would be difficult, inaccurate and even dangerous Better to cut a small piece away from a big piece
TS 200 C Table Saw with "Sliding Beam" The part of the table to the left of the saw blade can slide to and fro 600 mm on rollers. Jigs can be fixed to the T-section slot
Nob's puzzle – making the pieces Jig mounted on the sliding beam has a bar at 90 degrees and a V-groove at 82 degrees The bolt head engages with the T-slot
Nob's puzzle – making the pieces Square section stock, 40 mm x 40 mm, ripped on the table saw
Nob's puzzle – making the pieces The saw cuts part way through the jig. The stock is held in the V-groove, offset by 8 degrees. Note the end stop - a plastic "corner join" block and a bolt
Nob's puzzle – making the pieces When the cut is finished, the small half cube must not be free to move – it might jam between the rotating blade and the end-stop A plywood hold-down plate is used, secured with three screws. This anchors the half-cube at the end of the cut. There is not much contact area – the plate is the most secure method
The sequence of making the pieces First trim a number of pieces straight across, using the 90 degree guide Then, using the Vgroove: - slide a long piece up to the end-stop - secure it with the plate and screws - cut through, thereby making a half-cube - set aside the long piece for later trimming
A bandsaw project making a new puzzle from an old one Sam Loyd (1841 to 1911) was a great puzzler. His little books contain hundreds of original ideas. Here is one of his puzzles “Dissect a Greek cross and re-arrange the pieces to make a square. Do it with as few cuts as possible”
Making a new puzzle from an old one Here is Sam Loyd’s solution – only two cuts. And a nice “Aha!” moment. Interesting – but quite a lot of trouble for a puzzle that will be used only once. Can it be made better?
Making a new puzzle from an old one But cut one of the complicated pieces in two (making five in all). Now several more re-arrangements are possible And the woodwork is a bit easier
Making a new puzzle from an old one Make just one more cut (that makes six pieces) and a whole range of new shapes becomes possible
Making a new puzzle from an old one With a six piece puzzle, the pieces are easy to make and the number of nice shapes is over 30
Making a new puzzle from an old one The basic triangle behind the cross to square puzzle. Sides are 2, 1, and √ 5 (about 2. 236) Angles are 26 ½ and 63 ½ degrees (but let's calculate these numbers)
Making a new puzzle from an old one The sizes of the three triangles are in the ratio of 1 : 2 : √ 5. (remember Pythagoras? ) They fit together in unusual ways
Use the "cosine rule" and the cos-1 button on the calculator to calculate angles 2 (a 2 b – 2 c) cos(θ) = + / 2 ab a = 1. 0, b = √ 5 = 2. 236, c = 2. 0 cos(θ) = (1. 0 + 5. 0 – 4. 0) / 2 x 1. 0 x 2. 236 = 2. 0 / 4. 472 = 0. 4472 so θ = 63. 43°
Cutting the pieces for the new puzzle – jigs for the bandsaw The six pieces of the puzzle are cut from sheet that is 60 mm wide and about 8 mm thick. The angles of the triangles are 63 ½ , 23 ½ and 90 degrees
Cutting the pieces for the new puzzle – jigs for the bandsaw Several pieces 60 mm wide and 8 mm thick can be cut at the same time. The first jig is used to make the long cut at 63 ½ degrees. The others are used in sequence to produce all the pieces. Each jig is designed to be used with the rip fence set accurately at 60 mm
A puzzle made on the router The 6 -piece "burr" Burr puzzles all look alike from the outside, the complexity is in the details of the cuts This one is the simplest Three identical pieces Two identical pieces One solid piece
Six-piece "burr" puzzles Six blocks are needed for each puzzle – there are many ways of cutting the internal notches. In these pieces the notches go all the way through (so they can be cut by a router). This is not always the case.
Six-piece "burr" puzzles Six blocks are needed for each puzzle – in this case 25 mm x 75 mm There are four ways of making router cuts in the pieces. Two "outer" cuts (red and blue) and two "inner" cuts (green and yellow)
Six-piece "burr" puzzles The router jig has two position for holding the 75 mm pieces, one for an "outer" cut and one for an "inner" cut The cover holds the two pieces in place and prevents them rising up while the router is operating The bottom is attached to a dust extractor (not shown)
Six-piece "burr" puzzles The router sits on the cover and is guided by the side rails. To get a good finish the sides of each groove are pre-cut on the bandsaw A 12. 5 mm square end router bit is used for making the grooves
Using the lathe and the pillar drill A cylindrical "burr" Instead of square section pieces, this puzzle has six cylinders and a base. They are turned on the lathe and bored on the pillar drill
Six-piece cylindrical "burr" puzzle After turning, the cylinders are cross-bored (off-centre) in a jig to form the semi-circular depressions As before there are three identical pieces, two identical pieces and a solid piece
Six-piece cylindrical "burr" puzzle The base is also turned and bored (off-centre) on the lathe Using the base, the pieces may be re-assembled, like this
Puzzle Making for Woodworkers Donald Bell SFW Meeting, January 2011 Email : donald@marchland. org Web site : www. bellwoodwork. com
Some extra slides
Title: "Creative Puzzles of the World " Author(s): Pieter van Delft and Jack Botermans Publisher: over 1000 puzzles
Title: "Puzzle Projects for Woodworkers" Author(s): Allan Boardman Contains "Blockhead", "Nob's Never Ending Puzzle", six-piece burr etc
Title: "Puzzles Old and New – How to make and solve them" Author(s): Jerry Slocum and Jack Botermans A real classic, full of ideas Out of print, alas, maybe available second hand
Title: "The Book of Ingenious and Diabolical Puzzles" Author(s): Jerry Slocum and Jack Botermans They published a second book!
A wonderful web site – full of information about puzzles and books Just Google "rob's puzzle page" (the title bar looks the same upside down!)
Title: "Crafting Wood Logic Puzzles" Author(s): Charlie Self, Tom Lensch
Two classics by E M Wyatt (first published around 1928)
Title: "The Puzzling World of Polyhedral Dissections" Author(s): Stewart T Coffin Publisher:
“Pentomino” Puzzles A “domino” is made up of two squares So, a “tromino” has three And a “tetromino” has four There are 12 ways of arranging 5 joined up squares – the “Pentominoes”
“Pentomino” Puzzles Pentomino puzzles are very popular. They have a seeming endless variety of solutions. Here are the 12 pieces in rectangles
“Pentomino” Puzzles - variations Six of the pentominoes (on the left) can be made with 2 pieces of wood, size 2 and 3. The others are more complex.
“Pentomino” Puzzles The simplified set of six pentominoes can still make some interesting shapes.
“Pentomino” Puzzles Finding a good name for a puzzle is always important. Fortunately the shapes themselves suggest a name “SPLITV” – a bit hard to pronounce!
“Pentomino” Puzzles - SPLITV The puzzle leaflet is important but it requires quite a bit of work
“Pentomino” Puzzles - Tetrominoes The set of five tetrominoes cannot make a rectangle, but a double set can (and there are many solutions – so it’s a nice puzzle)
“Pentominoes” and “Hexiamonds” The word “pentomino” is like “domino” (made up of five squares, not two) So the word “hexiamond” is like “diamond” (made up of six triangles, not two) some of the shapes made with triangles
“Hexiamonds” There are 12 different arrangements of triangles possible. They make a nice (but difficult) puzzle that can be put together to make many shapes
“Tetriamonds” and “Pentiamonds” Four triangles can be put together in 3 ways to make “tetriamonds” And five triangles make 4 “pentiamonds” The shapes are quite easy to make
The “Delta” puzzle The 3 tetriamonds and 4 pentiamonds together make a set of 7 pieces that makes a good put-together “Delta” puzzle
The “Delta” puzzle The 3 tetriamonds and 4 pentiamonds together make a set of 7 pieces that makes a good put-together “Delta” puzzle with many possible shapes
The “Delta” puzzle And, as always, a leaflet has to be produced, something like this:
- Slides: 78
