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posted by martyb on Saturday September 02 2017, @09:04AM   Printer-friendly
from the simple!=easy dept.

Researchers at the University of St Andrews have thrown down the gauntlet to computer programmers to find a solution to a "simple" chess puzzle which could, in fact, take thousands of years to solve and net a $1M prize. Computer Scientist Professor Ian Gent and his colleagues, at the University of St Andrews, believe any program capable of solving the famous "Queens Puzzle" efficiently, would be so powerful, it would be capable of solving tasks currently considered impossible, such as decrypting the toughest security on the internet.

Devised in 1850, the Queens Puzzle originally challenged a player to place eight queens on a standard chessboard so that no two queens could attack each other. This means putting one queen in each row, so that no two queens are in the same column, and no two queens in the same diagonal. Although the problem has been solved by human beings, once the chess board increases to a large size no computer program can solve it.

The team found that once the chess board reached 1000 squares by 1000, computer progams could no longer cope with the vast number of options and sunk into a potentially eternal struggle akin to the fictional "super computer" Deep Thought in Douglas Adams' Hitchhiker's Guide to the Galaxy, which took seven and a half million years to provide an answer to the meaning of everything.

https://phys.org/news/2017-09-simple-chess-puzzle-key-1m.html

[Abstract]: "Complexity of n-Queens Completion"

[Source]: https://www.st-andrews.ac.uk/news/archive/2017/title,1539813,en.php

Any takers for this challenge?


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  • (Score: 0) by Anonymous Coward on Saturday September 02 2017, @10:26PM (1 child)

    by Anonymous Coward on Saturday September 02 2017, @10:26PM (#563037)

    (Serious)Why did you spend so much time commenting? Are you rich enough to pass on the prize? I'll assume you are. You sound smart enough to do this in maybe a weekend.

  • (Score: 3, Informative) by JoeMerchant on Sunday September 03 2017, @12:50AM

    by JoeMerchant (3937) on Sunday September 03 2017, @12:50AM (#563048)

    I took a run at NP back in college, my conclusion matches the literature: once you get all the terms of the problems, they're not simple at all. They're usually intractable search problems that involve pernicious edge cases.

    The researchers that posted this prize have a paper (I linked it somewhere else in the comments) where they describe how N-Queens transitions from P to NP as the number of pre-defined Queen positions increases - if no Queens are pre-placed on the board, you can find a solution rather easily, but at some point the problem becomes NP hard to determine if there is a solution or not, given the starting position. This is the game people used to pass around in the late 1800s: take a tough starting position and either find the solution or determine that there isn't one. Now that we know for certain all 12 solutions to the problem, you can classify any of the 4 billion+ 8 Queens starting problems by inspection, it (or a reflection or rotation) either matches one of the 12 solutions by inspection, or it doesn't. As N gets higher, the number of solutions grows roughly exponentially, and the current meme is that by N=1000, the problem (of finding all solutions) is intractable, therefore it is difficult to say if a plausible partial starting position has a workable solution or not.

    Some of the Clay prizes may still be up for grabs, but I don't think this one is - at least by conventional techniques. Maybe something with quantum computing might make it go faster, but I haven't heard about anybody trying to apply quantum techniques to NP, yet.

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