Eternity II Puzzle - History and Puzzle Construction

History and Puzzle Construction

The original Eternity puzzle was a tiling puzzle with a million-pound prize, created by Christopher Monckton. Launched in June 1999, it was solved by an ingenious 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.

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.