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Solve a 'Simple' Chess Puzzle, Win $1 Million (st-andrews.ac.uk)
An anonymous reader brings an important announcement:
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 $1 million 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. In a paper [PDF] published in the Journal of Artificial Intelligence Research today, the team conclude the rewards to be reaped by such a program would be immense, not least in financial terms with firms rushing to use it to offer technological solutions, and also a $1 million prize offered by the Clay Mathematics Institute in America.
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.
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.
"once the chess board increases to a large size no computer program can solve it"
How large is that? Many algorithms for simpler problems would fail if the size is multiplied by a big number.
Slashdot, fix the reply notifications... You won't get away with it...
First of all, the problem cant in any real sense be considered a chess puzzle, except in the superficial sense of placing queens on a board. Chess reasoning has nothing to do with a solution of the problem.
Second of all, the $1m prize is exactly the clay millennium prize for the resolution of P vs NP. If n-qeens has a solution in P, being NP-complete, this implies P=NP.
tldr Sensationalist title is sensationalist
I have discovered a truly remarkable program which this box is too small to contain. I'll complete it after I get back from a duel I have later today.
Three researchers proved that the queen problem is NP-complete. The prize is the millennium prize for P=NP. The journal publication is at http://jair.org/papers/paper5512.html.
Not only that, but if an 8-queen solution works on an 8x8 board, it'll work just as well on a 1000x1000 or a 10k x 10k board, etc. board. Move it over, put it in the same relative location in the 8x8 group at the corner of the larger board, done. So solve for 8x8 and move.
So you'll need to split that money with me, pal. :)
Of course, it's just slightly possible that TFS is not an accurate summary of the actual article / problem, but...
Nah. Besides, everyone knows that reading TFA is un-American. Even reading the summary raises red flags with Homeland Security, and may result in a National Security Letter (which you can read, but can't discuss.)
I've fallen off your lawn, and I can't get up.
"Quick" is defined in terms of how the running time for the solver scales with the size of the board. If you plot the time it takes to place N queens on an NxN board, you get an exponential curve for all currently known solvers. Either of two possibilities will result in winning $1 million:
1. Proving that this is the best one can do and that there are no better algorithms.
2. Finding a queens-placing algorithm whose running time is bounded by a polynomial function on N.
> Dr Jefferson added: “There is a $1,000,000 prize for anyone who can prove whether or not the Queens Puzzle can be solved quickly so the rewards are high.”
It's not the solution that gets you the prize, but the proof that the solution can be done quickly (without exploring nearly every permutation).
Often wrong but never in doubt.
I am Jack9.
Everyone knows me.
Yes it would. The Queen's Puzzle is an NP-complete problem, hence a solution to it would solve every other NP-complete problem.
Really cool in-browser visualizer of 5 different algorithms for solving this problem...
http://haseebq.com/n-queens-visualizer/
too bad that with Prolog solving the queen problem using CLP(FD) (using gprolog for instance) 500 queens can be solved in less than a second...
The problem is that, as the the paper shows, the n-queen problem is NP-complete, which in layman's terms means that the best algorithm that we know of would take exponential time to solve it.
To illustrate it, let's assume a hypothetical problem that has an (exponential) algorithm which takes 1 second to solve it with an input of 500 (queens or otherwise), and that the base of the exponent is 2 -- meaning that it would take 2 seconds to solve for an input of 501, 4 seconds for an input of 502, and so on.
Continuing the series, an input of 506 would take over a minute to solve, 512 will take over an hour, 517 over a day, 521 over a month, 525 over a year... In a million years you will be able to solve the problem with an input of 544. Are you seeing the picture?
Now the $1M prize is for either finding a polynomial complexity algorithm for solving that class of problems, or for a definite proof that one is not possible. Most mathematicians assume that the second outcome is correct, but no proof has been found, thus no $1M awarded.
This of course does not take into account quantum computing, but that's a different question.