Eternity puzzle

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 was distributed by the Ertl Company.

The puzzle consisted of filling a large almost regular dodecagon with 209 irregularly shaped smaller polygons. It was launched in June 1999, by Ertl Toys, marketed to amateur puzzle solvers 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.

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. According to Eternity's rules, possible solutions to the puzzle would be received by mail on September 21, 2000. If no correct solutions were opened, the mail for the next year would be kept until September 30, 2001, the process being repeated every year until 2003, after which no entries would be accepted.

Solution

The puzzle was solved on May 15, 2000, before the first deadline by two Cambridge mathematicians, Alex Selby and Oliver Riordan, who had used an ingenious technique to vastly accelerate their solution.cite web
url=http://www.archduke.org/eternity/method/desc.html
title=Description of (Eternity solver) method
work=Alex Selby (and Oliver Riordan)
date=2007-06-16
accessdate=2007-06-16] 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.

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 seven months of brute-force search on two domestic PCs. The puzzle's inventor said that the prize payout had forced him to sell his home; however, in 2006 this was revealed to be a publicity story.cite web
url=http://thescotsman.scotsman.com/scotland.cfm?id=121442007
title=Aristocrat admits tale of lost home was stunt to boost puzzle sales
work=The Scotsman
date=2007-01-24
accessdate=2007-01-24]

Future puzzles

Eternity II was launched in Summer 2007 with a prize of $2 million.

References

External links

* [http://news.bbc.co.uk/1/hi/entertainment/992393.stm BBC News report on the solution]
* [http://nrich.maths.org/public/viewer.php?obj_id=1354&part=index&refpage=articles.php An estimate of the complexity of the Eternity puzzle that turned out to be wrong]
* [http://plus.maths.org/issue13/features/eternity/index.html A detailed article on how the puzzle was solved]
* [http://mathpuzzle.com/eternity.html Discussion of the Eternity puzzle and related problems]
* [http://www.archduke.org/eternity/ Alex Selby's page on the Eternity puzzle]
* [http://mathworld.wolfram.com/Eternity.html Wolfram MathWorld article]