The 8-Queens Puzzle

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Image credit: Clay Mathematics Institute

Researchers during a University of St Andrews have thrown down a gauntlet to mechanism programmers to find a resolution to a “simple” chess nonplus that could, in fact, take thousands of years to solve and net a $1m prize. 

Computer Scientist Professor Ian Gent and his colleagues, during a University of St Andrews, trust any module able of elucidate a famous “Queens Puzzle” efficiently, would be so powerful, it would be able of elucidate tasks now deliberate impossible, such as decrypting a toughest confidence on a internet.

In a paper published in the Journal of Artificial Intelligence Research today, a organisation interpretation a rewards to be reaped by such a module would be immense, not slightest in financial terms with firms rushing to use it to offer technological solutions, and also a $1m esteem offering by a Clay Mathematics Institute in America.

Devised in 1850, a Queens Puzzle creatively challenged a actor to place 8 queens on a customary chessboard so that no dual queens could conflict any other. This means putting one black in any row, so that no dual queens are in a same column, and no dual queens in a same diagonal. Although a problem has been solved by tellurian beings, once a chess house increases to a immeasurable distance no mechanism module can solve it.

Professor Gent and his colleagues, Senior Research Fellow Dr Peter Nightingale and Reader Dr Christopher Jefferson, all of a School of Computer Science during a University, initial became intrigued by a nonplus after a crony challenged Professor Gent to solve it on Facebook.

The organisation found that once a chess house reached 1000 squares by 1000, mechanism progams could no longer cope with a immeasurable series of options and sunk into a potentially almighty onslaught same to a illusory “super computer” Deep Thought in Douglas Adams’ Hitchhiker’s Guide to a Galaxy, that took 7 and a half million years to yield an answer to a definition of everything.

Professsor Gent said: “If we could write a mechanism module that could solve a problem unequivocally fast, we could adjust it to solve many of a many critical problems that impact us all daily.

“This includes pardonable hurdles like operative out a largest organisation of your Facebook friends who don’t know any other, or really critical ones like enormous a codes that keep all a online exchange safe.”

The reason these problems are so formidable for mechanism programs, is that there are so many options to cruise that it can take many years.  This is due to a routine of “backtracking” – an algorithm used in programming where each probable choice is deliberate and afterwards “backed away” from until a scold resolution is found.

Dr Nightingale said: “However, this is all theoretical. In practice, nobody has ever come tighten to essay a module that can solve a problem quickly. So what a investigate has shown is that – for all unsentimental functions – it can’t be done.”

Dr Jefferson added: “There is a $1,000,000 esteem for anyone who can infer either or not a Queens Puzzle can be solved fast so a rewards are high.”

Chess has prolonged supposing a source for puzzles such as a normal myth of a menial who, when asked to select a prerogative by his king, asked for one pellet of rice to be placed on a initial block of a customary 8×8 chessboard, doubled in a subsequent and so on until it was found there was not adequate rice in a whole world.

The myth indicates a outrageous numbers concerned when regulating only a customary sized chess board. When a house distance increases a numbers turn vast.

There has been some difficulty about a $1m esteem offering by a Clay Mathematics Institute in America. Professor Ian Gent has created some comments about this indicate that were quoted by a Clay Maths Institute in a news object about a work, and that competence explain matters: https://claymath.org/events/news/8-queens-puzzle.

The paper ‘Complexity of n-Queens Completion‘ by Ian P Gent, Christopher Jefferson and Peter Nightingale is published in a 31 Aug 2017 emanate of Journal of Artificial Intelligence Research and is available online. DOI: doi:10.1613/jair.5512

An essay on a theme by Ian Gent, entitled ‘Why a world’s toughest maths problems are most harder than a chess puzzle, and good value US$1m‘, is published on The Conversation.

Visit the Clay Institute website for some-more information on a US$1m prize. 

Source: University of St Andrews

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