3.4 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Eternity II puzzle | 2/2 | https://en.wikipedia.org/wiki/Eternity_II_puzzle | reference | science, encyclopedia | 2026-05-05T11:03:02.845398+00:00 | kb-cron |
== History and design == The original Eternity puzzle was a tiling puzzle with a million-pound prize, created by Monckton. Launched in June 1999, it was solved by a computer search algorithm designed by Alex Selby and Oliver Riordan, which exploited combinatorial weaknesses of the original puzzle design. The prize money was paid out in full to Selby and Riordan. A puzzle with striking similarities to both eternity puzzles, the Diamond Dilemma, with a deadline in 1990, 10 years before the deadline of the original eternity puzzle, has fewer puzzle pieces, 160 compared with 209 and 256 for the first two eternity puzzles respectively, and yet Diamond Dilemma has not yet been solved in over 25 years. The Eternity II puzzle was designed by Monckton in 2005, this time in collaboration with Selby and Riordan, who designed a computer program that generated the final Eternity II design. According to the mathematical game enthusiast Brendan Owen, the Eternity II puzzle appears to have been designed to avoid the combinatorial flaws of the previous puzzle, with design parameters which appear to have been chosen to make the puzzle as difficult as possible to solve. In particular, unlike the original Eternity puzzle, there are likely only to be a very small number of possible solutions to the problem. Owen estimates that a brute-force backtracking search might take around 2×1047 steps to complete. Monckton was quoted by The Times in 2005 as saying:
"Our calculations are that if you used the world's most powerful computer and let it run from now until the projected end of the universe, it might not stumble across one of the solutions." Although it has been demonstrated that the class of edge-matching puzzles, of which Eternity II is a special case, is in general NP-complete, the same can be said of the general class of polygon packing problems, of which the original Eternity puzzle was a special case. Like the original Eternity puzzle, it is easy to find large numbers of ways to place substantial numbers of pieces on the board whose edges all match, making it seem that the puzzle is easy. However, given the low expected number of possible solutions, it is presumably astronomically unlikely that any given partial solution will lead to a complete solution.
== See also == TetraVex, a similar simpler (no piece rotation or border pieces) edge-matching puzzle game from the Microsoft Entertainment Pack, shown to be NP-complete. Wang tiles
== References ==
== External links ==
Official website (archived) Flash demo of a 4x4 puzzle from the original (now defunct) website (archived) Online solution visualizer Eternity II discussion forum (Groups.io) Description of Eternity II and discussion of solvers Description of Louis Verhaard's Eternity II solver used by Anna Karlsson Description of the similar puzzle Diamond Dilemma Software:
Open Source Matlab Eternity II Solver Open Source Eternity II Editor/Solver software Open Source Eternity II puzzle software E2Lab : Free Eternity II Editor/Solver software E2Solver : Open Source Eternity II puzzle solver Android app for Eternity II type edge matching puzzles. iPhone and iPad app for Eternity II type edge matching puzzles.