August 2001 edition
Click here to see the May 2000 edition. (PentaSlimbes, PolyBiSquares, PolySquareRhombi, PolyBricks, DualOctagonSquares, FourStars&Pentagons, HexagonRhombi, DualStarHexSquares, PolyTriForms, TetraFrogs)
Click here to see the Aug 2000 edition. (Hexagon by Zucca's Puzzle, PolyDoms , Big Pizza, Kites & Bricks, DomSlicedPolyominoes, PolyPenroses, Sexominoes Number Five, Poly-Arc-Iamonds, More about PolyCairos)
Click here to see the Mar 2001 edition. (PolyBricks solutions, Break & Paste Polyforms, PolyWorms, TetraSticks)
- The Domino Puzzle with perimeter=10.
- The 8x8 square puzzle of TSOB.
- The 120 Sexominoes Number Five 12x10 rectangle.
- The minimizing of the pipes number of the Tubominoes.
- The 120 Sexominoes Number Five cover a cube.
- 5 Tetrominoes + 7 Biarc + 22 Triarc by Henri Picciotto cover a cube.
- The Octiamonds cover a tetrahedron.
- The Heptiamonds cover a octahedron.
- The Isoiamonds(8) cover two tetrahedrons.
- The 36 PentaSquares in a simmetrical box.
- The Hexominoes cover a cube with edge=sqr(34)
Once upon a time there was an ellipse. When R/r became sqr(3) he was able to arrange this crossed lattice and was tangent to the other ellipsis:
The forms joined five to five and 16 PentaElles had born:
Will they be able to cover the shape below?
I built a software for solving polyminoes problems which uses the Gerard Putter Java Engine. The merit is all of Gerard, but with my SW, it is more easy. You could design the polyminoes and the shapes. It produces a HTML file with all the parameters for the Gerard's Engine.
It runs on MS Windows95 or better with Internet Explorer 5.0 or better. You could download the compact form here [67KB]. It's possible you don't have a DLL file. In this case you must to download the complet setup program here [1.5MB].
It was then necessary to codify the pieces as polyominoes:
It was easy fixing the central red square on the shape. The Gerard's Engine produced the solution:
And I have redrawn it so:
If you rectify the edges, you get polyforms which could be inserted into an exact rectangle:
In this case the lattice remember us the Pentagonal Cairo Tasselation, crossed with a square grid. This puzzle has 17 different solutions.
Sept 4th, 2001
Brendan Owen did some counts:
... and he has found this solution for the 28 one-side pentellys:
He has transformed them into poly-checkered-mini-tans on checkered triangle grid. See here his original solution.
Below there are the 22 PolyOctagonSquares defined as:
They can fit into this shape. At right the solution by coding the poliforms as polyominoes on Gerard's Solver.
Do you remember the 80 TriOctagonSquares (where nr. of octagons = nr. of squares = 3) which Brendan Owen calculated? I think it's the time for a solution :o)
I'll publish the first. Below a possible shape:
Sep 24, 2001
Alessandro Fogliati solved BIBLICAL, the 666 Pieces Math Puzzle witch can cover a 18x37 rectangle:
It isn't trivial!
First edition: Aug 28th, 2001 - Last revision: Sept 26th, 2001
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| PENTOMINOES |
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| POLYSEXES |
| Sexominoes | Xominoes | Zucca's Puzzle | Domino Puzzle | SexCubes | Dodecaculeus | Tubominoes |
| SEXEHEXES |
| SexeHexeS For Sale | More about SexeHexeS | How we did it | Other Sexehex Puzzle | My Solution | Reproduction |
| POLYMULTIFORMS |
| Mar 2001 edition | Aug 2000 edition | May 2000 edition | PolyEdges | To cover a solid | Fourier Series of a Square | Order 13 Perfect Square | Fibonacci Machine |