A bandsaw projectmaking 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 oneBut cut one of the complicated pieces in two (making five in all).Now several more re-arrangements are possibleAnd 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

cos(θ) = (a2 + b2 – c2) / 2aba = 1.0, b = √5 = 2.236, c = 2.0cos(θ) = (1.0 + 5.0 – 4.0) / 2 x 1.0 x 2.236

= 2.0 / 4.472 = 0.4472so θ = 63.43°

Use the "cosine rule" and the cos-1 button on the calculator to

calculate angles

Cutting the pieces for the new puzzle – jigs for the bandsaw

The six pieces of the puzzle are cut from sheet that is 60mm wide and about 8mm 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 60mm wide and 8mm 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 60mm

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 cutsThis one is the simplest

Three identical piecesTwo identical piecesOne 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 case25mm x 25mm x 75mm

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 75mm 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 12.5mm 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" puzzleAfter 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 BellSFW Meeting, January 2011

Email : donald@marchland.orgWeb site : www.bellwoodwork.com