# 'Simple' chess puzzle holds key to $1m prize

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.

In a paper 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 $1m 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.

Professor Gent and his colleagues, Senior Research Fellow Dr Peter Nightingale and Reader Dr Christopher Jefferson, all of the School of Computer Science at the University, first became intrigued by the puzzle after a friend challenged Professor Gent to solve it on Facebook.

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.

Professsor Gent said: "If you could write a computer program that could solve the problem really fast, you could adapt it to solve many of the most important problems that affect us all daily.

"This includes trivial challenges like working out the largest group of your Facebook friends who don't know each other, or very important ones like cracking the codes that keep all our online transactions safe."

The reason these problems are so difficult for computer programs, is that there are so many options to consider that it can take many years. This is due to a process of "backtracking" – an algorithm used in programming where every possible option is considered and then "backed away" from until the correct solution is found.

Dr Nightingale said: "However, this is all theoretical. In practice, nobody has ever come close to writing a program that can solve the problem quickly. So what our research has shown is that – for all practical purposes – it can't be done."

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."

Chess has long provided the source for puzzles such as the traditional fable of the servant who, when asked to choose a reward by his king, asked for one grain of rice to be placed on the first square of a standard 8x8 chessboard, doubled in the next and so on until it was found there was not enough rice in the entire world.

The fable indicates the huge numbers involved when using just a standard sized chess board. When the board size increases the numbers become vast.

**More information:**Complexity of n-Queens Completion.

*Journal of Artificial Intelligence Research*. DOI: DOI: 10.1613/jair.5512 , http://jair.org/papers/paper5512.html

**Citation**: 'Simple' chess puzzle holds key to $1m prize (2017, September 1) retrieved 22 August 2019 from https://phys.org/news/2017-09-simple-chess-puzzle-key-1m.html

## User comments

dirk_bruerecturner3rdHyperfuzzybaudrunnerwith the checkerboard rows counted from the top, columns left to right..

n = the row number

x = the tile number to place the queen

for even values of n beginning with row 2: x = n / 2 up to the last row, then to continue,

starting with row 1, and for all subsequent odd numbered rows: x = x + 1. You can see the pattern.

One solution for an 8 x 8 board (does not follow the above method): places the queens as follows..

row - column

1 - 6

2 - 1

3 - 5

4 - 2

5 - 8

6 - 3

7 - 7

8 - 4

Whydening GyreThe article already says in can be solved by humans.

It's just that programming a 'puter to recognize and check is really tuff...

And they're talking in context of 1000x1000, not 8x8 or 10x10.

AlexisTMmonstercolorfunbaudrunnerThe 10x10 solution I provided is really easy to implement and is portable to all larger layouts, like I said, with some minor adaptations for even or odd numbers of rows - eg. a 100x100 cell layout, or a 11x11 layout. Population is immediate, and needs no verification from the software. There are military applications, example is distribution of drones over a large area.

The math groupies want a complex answer that they can't understand in order to get any respect from them. "The math groupie not a mathematician be."

Occam's razor, my friend.

They'll never give me the money, though. They're Scots!

baudrunnerO O O O O M O O

M O O O O O O O

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wetnosegvnsreddyYes, it is fast enough.

Please publish the solution for a queen at (1,1) preplaced.

Please mention, what is the programming language used.

HyperfuzzyWhy would it take so long, each queen owns a set of squares, eliminated from search. The next location is obviously a Knight move away, in one direction until no more exist! A simple elimination game. By the way, count the number of retrys. The software you're using sounds very inefficient, it's simply an array filled game while maximizing the number of queens. You can see that the number of queen is always equal or less than the square-root of number of cells. So if an N sided board there are N^3 try's using a draconian method per queen on a decreasing set of plys, mirro

HyperfuzzyHyperfuzzyInitiate Constant Strings

a plys Q(a1), Q(a2). ... Q(nn); Note: each ply is a string of 1's and 0' or as N^2 Bit register.

For all plys

If rowA<>RowB and ColA<>ColB and no Match from StringA, StringB, keep

Display Board

Done once

Something like that ought to do it. Note: I would seek to eliminate the embedded loops.

HyperfuzzybrosalesHyperfuzzySee what I just did, I let every square see every other square and they have a way of being choosy where a new neighbor lives, so these squares are off limits; so first square suggest a set and the set suggest ... only until no suggestions are left, report solution set. I know you gonna blow it first try, coding, so buggy, why do we do this to ourselves? Create human language interface. So what if you must be logical and tabulate what's omitted, ha, ha

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