The Great Pyramid Puzzle is a puzzle consisting of a tetrahedral body, and 81 loose triangular tiles that are coloured with red and white patterns. The tiles can be stuck onto the tetrahedron, nine tiles on each face, because every tile has a peg in its centre and the tetrahedron has holes they fit into. The aim is to cover the tetrahedron with the tiles such that all adjacent tiles match along their common edge.
There is also a smaller version with 4 tiles on each face, 16 tiles all together, which is called the Great Pyramid Pocket Puzzle.
The tiles are regular triangles, which are split into 12 segments by 6 lines - the 3 bisectors and 3 lines parallel to the sides. The four segments along each side are coloured either red or white. The following pictures show all the tiles of both puzzles:
The Great Pyramid Puzzle:
The Great Pyramid Pocket Puzzle:
The puzzles were made by Eliot Inventions Ltd. in 1981. The pocket puzzle comes in a neat transparent plastic box that opens in an unusual way.
The puzzle's 81 tiles can be arranged in 81! ways, and oriented in 381 ways.
A tetrahedron has 12 orientations, so the Great Pyramid Puzzle has 81!·381/12
= 3.0847·10160 possible arrangements for the tiles.
The pocket puzzle's 16 tiles can be arranged in 16! ways, and oriented in 316 ways.
The Pocket Puzzle therefore has 16!·316/12 = 75,054,791,570,863,104,000
possible arrangements for the tiles.
This is of course not a realistic measure of difficulty, since you would not continue placing tiles
after one tile is wrongly positioned.
One of the many solutions to the Great Pyramid Puzzle is shown below.
I used my computer to find all solutions of the Pocket puzzle, and there are 87 of them.They are all shown below. To save space, if some solutions differ only by two or three tiles then only one of them is shown and the relevant tiles are given a different colour. The number of solutions represented by the drawing is also given.
