In three cubepuzzle, please note: ６^{3}＝５^{3}＋４^{3}＋３^{3}（＝２１６） This puzzle is to devide a side 6 cube into a side 5 cube, a side 4cube and a side 3 cube. 216 cubes unit is easily devide, however all different 37 kinds of pieces whose total is 216 should be pre- pared. First of all, compose a side 6 cube. Then, split into three cubes, a side 5 cube, a side 4 cube and 3 side cube using the 37 pieces. It would be absolutely difficult and it seems al- most impossible to compose 3 cubes using all the 37 pieces at the same time. So, after painstaking efforts when you can achieve, you would be breath-taken and very much impressed with beautiful docking of puzzle and mathematics.## Reason why the Pieces are 37.

## When we connect a regular square with a side and a side: ２ pieces １ kind （Domino ） ３ 〃 ２ Kinds （Tromino ） ４ 〃 ５ 〃 （Tetoromino） ５ 〃 １２ 〃 （Pentomino ） ６ 〃 ３５ 〃 （Hexomino ） of pieces are made. These are generally called "Polyominoes". Three cube Puzzule are made by connecting 6 squares to make 35 pieces which are called "Hexomino", and further developed into a solid cube by adding thickness of a side of the square. Total number of unit cube com- posed by 35 kinds of pieces are 6×35 ＝ 210. When a side 6 cube is composed by unit cube, it is: 6×6×6 ＝ 216 and 6 short. Another problem. In 35 kinds of pieces, there is a piece which is made by connecting 6 unit cube straight. This particular piece is excluded because it can not be used exdcept a side 6 cube. Therefore, 12 pieces are short. This shortage is filled with 3 unit cubes; a piece connected 3 pieces straight,4 pieces straight and 5 pieces straight, then total number of pieces are 37.

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## Usage of Three Cube Puzzle by Plane

Three cube puzzle is made as cubic subject. However, it is also used as "Flat(Plane) puzzle" making squares and other figures, and you will enjoy much more variation than the basic "Hexomino Puzzle". The basic "Hexomino Puzzle" could not be made square figure(15x14, 21x10 etc.) To certify this is easy and if you are interested, Please ask me by E-mail. I will answer you by E-mail. Regarding Three Cube Puzzle, no such limitation and can make not only squares but can make various figures. But, to make six 6x6 regular squares will be most interesting. At this moment, two solutions are found. it is as difficult and beautiful as the puzzle which devides a side 6 cube into three cubes.Now, back to the table of Contents

## Pentomino Puzzule

Among Polyomino Puzzule, Pentomino is most popular. A puzzule which got a hint from flat pentomino is now in the market from Tenyo Co.,Ltd. Also a HOME PAGE regarding pentomino is available: Flat Pentomino by Zinc's home page. Cubic Pentomino by Yoshibei's home pageNow, back to the table of Contents

## How this puzzle was created, etc

It is well Known ３^{２}＋４^{２}＝５^{２}, natural number solution by Pythagorean theorem. However, ３^{３}＋４^{３}＋５^{３}＝６^{３}is not so well known. Honestly speaking, I did not Know either. One day at a book store, I bought a book, "Sosuuyakyoku" and found out the abobe fact.. Then, I was deeply impressed with beautiful and interesting relation of consecutive numbers, which gave me a hint to create something and "Pentomino" occurred to be happend in my mind. and after much turns and twists,"Three Cube Puzzle"was born. In present from, pieces which are made by connecting unit squares straight are 37 kinds, the lengths are 3, 4 and 5, 3 types. At the beginning, they were 5 types 1, 2, 2, 3 and 4 and 39 kinds. then at next stage, 4 types 2, 3, 3 and 4 - 38 kinds. At the last stage, it became to present form, 37 sorts. The reason is that the minimum pieces are 37 pieces as far as the base is Hexomino. The less the pieces are, the less the solution are and hard to get. Myself also could not find the solution. For your information, so far the composition pattern to compose 3 cubes at the same time exists only two method. It is unKnown how many methods exist. Your challenge is welcome.Now, back to the table of Contents

## Introduction of our products:

All hand made and Natural wood. You can feel wormth of wood and it will be a nice decoration on your desk. The details are as follows: Spruce : \ 7.000 American white ceder : \ 8.000 Japanese Oak : \ 12.000 Ebony : \ 50.000 Rosewood : \ 50.000 Besides three cube puzzle, a regular square puzzle is also available at:

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