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. All the polygons had the same color and had between seven and eleven sides.

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 it would take at least 3 years before anyone could crack the puzzle.

One estimate made at the time stated that the puzzle had 10500 possible attempts at a solution, and it would take longer than the lifetime of the Universe to calculate all of them even if you had a million computers.

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.

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 these 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 falsely claimed in 2000 that the earlier-than-expected discovery had forced him to sell his 67-room house to pay the prize.

In 2006 he revealed by his own will that the claim had been a PR stunt to boost sales over Christmas, that the house’s sale was unrelated, and that he was going to sell it anyway.