Eternity II puzzle
The Eternity II puzzle, aka E2 or E II, is a puzzle competition which was released on 28 July 2007. It was published by Lord Christopher Monckton, and is marketed and copyrighted by TOMY UK Ltd. A $2 million prize was offered for the first complete solution. The competition ended at noon on 31 December 2010, with no solution being found.
The Eternity II puzzle is an edge-matching puzzle which involves placing 256 square puzzle pieces into a 16 by 16 grid, constrained by the requirement to match adjacent edges. It has been designed to be difficult to solve by brute-force computer search.
Each puzzle piece has its edges on one side marked with different shape/colour combinations (collectively called "colours" here), each of which must match precisely with its neighbouring side on each adjacent piece when the puzzle is complete. The other side of each piece is blank apart from an identifying number, and is not used in the puzzle. Thus, each piece can be used in only 4 orientations. There are 22 colours, not including the gray edges. Five of those can only be found on border and corner pieces and 17 only on so called inner pieces and the side of the border piece across from the gray colour. This puzzle differs from the first Eternity puzzle in that there is a starter piece which must be placed near the center of the board. (See PDF rulebook on official website.)
Two Clue Puzzles were available with the launch of the product, which, if solved, each give a piece position on the main 256-piece puzzle. Clue Puzzle 1 is 6 by 6, with 36 pieces and Clue Puzzle 2 is 12 by 6, with 72 pieces. Two further puzzles were made available in 2008. Clue Puzzle 3 is 6 by 6, with 36 pieces, and Clue Puzzle 4 is 12 by 6, with 72 pieces.
The number of possible configurations for the Eternity II puzzle, assuming all the pieces are distinct, and ignoring the fixed pieces with pre-determined positions, is 256! × 4256, roughly 1.15 × 10661. A tighter upper bound to the possible number of configurations can be achieved by taking into account the fixed piece in the center and the restrictions set on the pieces on the edge: 1 × 4! × 56! × 195! × 4195, roughly 1.115 × 10557. A further upper bound can be obtained by considering the position and orientation of the hint pieces obtained through the clue puzzles. In this case the position and orientation of five pieces is known, giving an upper bound of 4! × 56! × 191! × 4191 = 3.11 × 10545, yielding a search space 3.70 × 10115 times smaller than the first approximation.
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