Eternity puzzle
Encyclopedia
Eternity is a tiling puzzle
created by Christopher Monckton
and launched by the Ertl Company
in June 1999. Consisting of 209 pieces, it was marketed as being practically unsolveable, with a £1 million prize on offer for whoever could solve it within four years. The prize was paid out in October 2000 for a winning solution arrived at by two mathematicians from Cambridge
. A second puzzle, Eternity II
, was launched in Summer 2007 with a prize of US$2 million.
with 209 irregularly shaped smaller polygon pieces of the same color. All the pieces were made from a combination of equilateral triangles and half-triangles, with each piece having the same total area of 6 of those triangles, and between seven and eleven sides.
, put up half the prize money himself, the other half being put up by underwriters in the London insurance market. 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.
Before marketing the puzzle, Monckton had thought that it would take at least three 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.
Once solved, Monckton jokingly claimed that the earlier-than-expected solution had forced him to sell his 67-room house to pay the prize. Unprompted, in 2006, he disclosed 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.
The puzzle was solved on May 15, 2000, before the first deadline, by two Cambridge
mathematicians, Alex Selby and Oliver Riordan. Key to their success was the mathematical rigour with which they approached the problem of determining the tileability of individual pieces and of empty regions within the board. These provided measures of the probability that a given piece could help to fill or 'tile' a given region, and the probability that a given region could be tiled by some combination of pieces. In the search for a solution, these probabilities were used to identify which partial tilings, out of a vast number explored by the computer program, were most likely to lead to a solution. A complete solution was obtained within seven months of brute-force search
on two domestic PCs.
Tiling puzzle
Tiling puzzles are puzzles involving two-dimensional packing problems in which a number of flat shapes have to be assembled into a larger given shape without overlaps . Some tiling puzzles ask you to dissect a given shape first and then rearrange the pieces into another shape...
created by Christopher Monckton
Christopher Monckton, 3rd Viscount Monckton of Brenchley
Christopher Walter Monckton, 3rd Viscount Monckton of Brenchley is a British politician, public speaker, former newspaper editor and hereditary peer. Formerly a member of the Conservative Party, Monckton has been the Head of the Policy Unit for the UK Independence Party since November 2010. He was...
and launched by the Ertl Company
Ertl Company
The Ertl Company is an American toy company best known for its die-cast metal alloy collectible replicas of farm equipment and vehicles. The company is based in Dyersville, Iowa, home of the National Farm Toy Museum...
in June 1999. Consisting of 209 pieces, it was marketed as being practically unsolveable, with a £1 million prize on offer for whoever could solve it within four years. The prize was paid out in October 2000 for a winning solution arrived at by two mathematicians from Cambridge
Cambridge
The city of Cambridge is a university town and the administrative centre of the county of Cambridgeshire, England. It lies in East Anglia about north of London. Cambridge is at the heart of the high-technology centre known as Silicon Fen – a play on Silicon Valley and the fens surrounding the...
. A second puzzle, Eternity II
Eternity II puzzle
The Eternity II puzzle, aka E2 or E II, is a puzzle competition which was released on 28 July 2007.The competition ended at noon on the 31st of December 2010.It was published by Christopher Monckton, and is marketed and copyrighted by TOMY UK Ltd...
, was launched in Summer 2007 with a prize of US$2 million.
Puzzle
The puzzle consists of filling a large almost regular dodecagonDodecagon
In geometry, a dodecagon is any polygon with twelve sides and twelve angles.- Regular dodecagon :It usually refers to a regular dodecagon, having all sides of equal length and all angles equal to 150°...
with 209 irregularly shaped smaller polygon pieces of the same color. All the pieces were made from a combination of equilateral triangles and half-triangles, with each piece having the same total area of 6 of those triangles, and between seven and eleven sides.
Retail
The puzzle was launched in June 1999, by Ertl, 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.Prize
The puzzle's inventor Christopher MoncktonChristopher Monckton, 3rd Viscount Monckton of Brenchley
Christopher Walter Monckton, 3rd Viscount Monckton of Brenchley is a British politician, public speaker, former newspaper editor and hereditary peer. Formerly a member of the Conservative Party, Monckton has been the Head of the Policy Unit for the UK Independence Party since November 2010. He was...
, put up half the prize money himself, the other half being put up by underwriters in the London insurance market. 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.
Before marketing the puzzle, Monckton had thought that it would take at least three 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.
Once solved, Monckton jokingly claimed that the earlier-than-expected solution had forced him to sell his 67-room house to pay the prize. Unprompted, in 2006, he disclosed that the claim had been a PR
Public relations
Public relations is the actions of a corporation, store, government, individual, etc., in promoting goodwill between itself and the public, the community, employees, customers, etc....
stunt to boost sales over Christmas, that the house's sale was unrelated, and that he was going to sell it anyway.
Solution
As soon as the puzzle was launched, an online community emerged devoted to solving it, centred on a mailing list on which many ideas and techniques were discussed. It was soon 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. Computer searches were carried out to find which pieces tiled well or badly, and this data used to alter otherwise-standard backtracking search programs to use the bad pieces first, in the hope of being left with only good pieces in the hard final part of the search.The puzzle was solved on May 15, 2000, before the first deadline, by two Cambridge
Cambridge
The city of Cambridge is a university town and the administrative centre of the county of Cambridgeshire, England. It lies in East Anglia about north of London. Cambridge is at the heart of the high-technology centre known as Silicon Fen – a play on Silicon Valley and the fens surrounding the...
mathematicians, Alex Selby and Oliver Riordan. Key to their success was the mathematical rigour with which they approached the problem of determining the tileability of individual pieces and of empty regions within the board. These provided measures of the probability that a given piece could help to fill or 'tile' a given region, and the probability that a given region could be tiled by some combination of pieces. In the search for a solution, these probabilities were used to identify which partial tilings, out of a vast number explored by the computer program, were most likely to lead to a solution. A complete solution was obtained within seven months of brute-force search
Brute-force search
In computer science, brute-force search or exhaustive search, also known as generate and test, is a trivial but very general problem-solving technique that consists of systematically enumerating all possible candidates for the solution and checking whether each candidate satisfies the problem's...
on two domestic PCs.