{"id":24847,"date":"2014-06-01T16:46:08","date_gmt":"2014-06-01T21:46:08","guid":{"rendered":"http:\/\/blogs.ams.org\/mathgradblog\/?p=24847"},"modified":"2014-06-16T17:59:37","modified_gmt":"2014-06-16T22:59:37","slug":"eternity-ii-puzzle-unsolved","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/mathgradblog\/2014\/06\/01\/eternity-ii-puzzle-unsolved\/","title":{"rendered":"The Eternity II Puzzle: Still Unsolved!!"},"content":{"rendered":"
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Photo Credit: Karen Carr<\/p><\/div>\n

Between the light and darkness of mathematical knowledge exists an ever-extending boundary that pushes\u00a0the limits of abstraction into the framework of tangible existence.\u00a0\u00a0 What can and cannot be known converges with each symbol in a collection of coherent logic.\u00a0\u00a0 Step after step of pure reasoning reveals an underlying component connecting complexity with simplicity.\u00a0 Oftentimes, this sought after link is not easily discovered.\u00a0 This is immediately true for the ever-growing list of proposed problems that span the entire spectrum of mathematics.<\/p>\n

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This notion also holds true for problems and puzzles that pose a more recreational nature. \u00a0 I was introduced to one such puzzle during a talk given by the English mathematician Oliver Riordan during my undergrad years at the University of Memphis. \u00a0 Riordan was presenting the methods he and his colleague, mathematician Alex Selby, used to solve the first version of the conundrum known as the Eternity Puzzle.\u00a0 In late 2000, with a combination of intuition, combinatorial reasoning, and statistical inference, Riordan and Selby were able to place all 209 irregularly fashioned pieces of the puzzle in a dodecagon shaped board and claimed the \u00a31 million prize from the puzzle\u2019s inventor, \u00a0Lord Christopher Monckton.<\/p>\n

This was somewhat of a shock since the Eternity Puzzle has an estimated \"10^{500}\" combinations and it would take anyone using brute force computation longer than the entire age of the Universe to compute all possible combinations in hopes of finding a solution. \u00a0However, mathematics is an employable tool often used to supplant computational complexity.\u00a0 Such was the case with the solution to the Eternity Puzzle.<\/p>\n

With the success of selling over 500,000 copies of the first puzzle, Monckton recruited Riordan and Selby to help invent a second version of the puzzle known as the Eternity II Puzzle.\u00a0\u00a0 Unlike the first version, the Eternity II is very much unsolved.\u00a0\u00a0\u00a0 The only people that know of a solution are its creators.\u00a0\u00a0\u00a0 Also, unlike the first version, there are 256 square pieces with designs in four directions such that any solution on the 16 x 16 gridded board must preserve a pairwise edge-matching in every direction (see above picture).\u00a0\u00a0 From its release in 2007, a $2 million prize was offered for its solution that has since expired in 2010.<\/p>\n

When I graduated from the University of Memphis, some administrators in the math department gave me one of the copies of the puzzle that Riordan brought with him for the talk.\u00a0\u00a0 On several occasions I have attempted to solve it with no success.\u00a0\u00a0 Maybe one day a solution will emerge from the depths of complexity into the realm of simplicity.<\/p>\n

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Between the light and darkness of mathematical knowledge exists an ever-extending boundary that pushes\u00a0the limits of abstraction into the framework of tangible existence.\u00a0\u00a0 What can and cannot be known converges with each symbol in a collection of coherent logic.\u00a0\u00a0 Step … Continue reading →<\/span><\/a><\/p>\n

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