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The eternity puzzle was a geometric puzzle with a million-pound prize, created by Christopher Monckton, who put up half the money himself, the other half being put up by underwriters in the London insurance market.
The puzzle consisted of filling a large almost regular dodecagon with 209 smaller irregularly shaped smaller polygons. It was marketed to amateur puzzle solvers by Ertl Toys, and 500,000 copies were sold worldwide, with the game becoming a craze at one point. Eternity was the best-selling puzzle or game in the UK at its price-point of £35 in its launch month. It was voted Puzzle of the Year in Australia. It sold in record numbers even in Greenland. A regular dodecagon A dodecagon is a polygon with exactly twelve sides. ...
Before marketing the puzzle, Monckton had thought that the puzzle would probably be solved within 1 to 3 years. One estimate made at the time stated that the puzzle would probably take longer than the lifetime of the Universe to solve.
The puzzle was solved before the deadline by two Cambridge mathematicians, Alex Selby and Oliver Riordan, who had used an ingenious technique vastly to accelerate their solution. They realised that it was trivial to fill the board almost completely, to an "end-game position" where an irregularly-shaped void had to be filled with only a few pieces, at which point the pieces left would be the "wrong shapes" to fill the remaining space. The hope of solving the end-game depended vitally on having pieces that were easy to tile together in a variety of shapes. Map of the Cambridgeshire area (1904) The city of Cambridge is an old English university town and the administrative centre of the county of Cambridgeshire. ...
They started a computer search to find which pieces tiled well or badly, and then used this data to alter their otherwise-standard backtracking search program to use the bad pieces first, in the hope of being left with only good pieces in the hard final part of the search. This heuristic approach paid off rapidly, with a complete solution being obtained within a couple of months of brute-force search on a couple of domestic PCs. Backtracking is a strategy for finding solutions to constraint satisfaction problems. ...
Heuristic is the art and science of discovery and invention. ...
In computer science, a brute-force search consists of systematically enumerating every possible solution of a problem until a solution is found, or all possible solutions have been exhausted. ...
Eternity II, designed by Monckton in collaboration with the two solvers of Eternity, is planned to launch at Christmas 2007 with a prize of $2 million.
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