Emerging Technology from the arXiv

A View from Emerging Technology from the arXiv

Best of 2012: Mathematicians Solve Minimum Sudoku Problem

In January, a year-long calculation proved there are no 16-clue puzzles in Sodoku, confirming the long held belief that the smallest number of starting clues a puzzle can contain is 17

  • December 27, 2012

“Sudoku is a number puzzle consisting of a 9 x 9 grid in which some cells contain clues in the form of digits from 1 to 9. The solver’s jobs is to fill in the remaining cells so that each row, column and 3×3 box in the grid contains all nine digits.

There’s another unwritten rule: the puzzle must have only one solution. So grids cannot contain just a few starting clues.

It’s easy to see why. A grid with 7 clues cannot have a unique answer because the two missing digits can always be interchanged in any solution. A similar argument explains why grids with fewer clues must also have multiple solutions.

But it’s not so easy to see why a grid with 8 clues cannot have a unique solution, or indeed one with 9 or more clues.

That raises an interesting question for mathematicians: what is the minimum number of Sudoku clues that produces a unique answer?

This is a question that has hung heavy over the Sudoku community, not least because they think they know the answer. Sudoku fanatics have found numerous examples of grids with 17 clues that have a unique solution but they have never found one with 16 clues.

That suggests the minimum number is 17 but nobody has been able to prove that there isn’t a 16-clue solution lurking somewhere in puzzle space.

Enter Gary McGuire and pals at University College Dublin. These guys have solved the problem using the tried and trusted mathematical technique of sheer brute force.

Continued…

Cut off? Read unlimited articles today.

Become an Insider
Already an Insider? Log in.

Uh oh–you've read all of your free articles for this month.

Insider Premium
$179.95/yr US PRICE

Want more award-winning journalism? Subscribe and become an Insider.
  • Insider Premium {! insider.prices.premium !}*

    {! insider.display.menuOptionsLabel !}

    Our award winning magazine, unlimited access to our story archive, special discounts to MIT Technology Review Events, and exclusive content.

    See details+

    What's Included

    Bimonthly home delivery and unlimited 24/7 access to MIT Technology Review’s website.

    The Download. Our daily newsletter of what's important in technology and innovation.

    Access to the Magazine archive. Over 24,000 articles going back to 1899 at your fingertips.

    Special Discounts to select partner offerings

    Discount to MIT Technology Review events

    Ad-free web experience

    First Look. Exclusive early access to stories.

    Insider Conversations. Listen in as our editors talk to innovators from around the world.

  • Insider Plus {! insider.prices.plus !}* Best Value

    {! insider.display.menuOptionsLabel !}

    Everything included in Insider Basic, plus ad-free web experience, select discounts to partner offerings and MIT Technology Review events

    See details+

    What's Included

    Bimonthly home delivery and unlimited 24/7 access to MIT Technology Review’s website.

    The Download. Our daily newsletter of what's important in technology and innovation.

    Access to the Magazine archive. Over 24,000 articles going back to 1899 at your fingertips.

    Special Discounts to select partner offerings

    Discount to MIT Technology Review events

    Ad-free web experience

  • Insider Basic {! insider.prices.basic !}*

    {! insider.display.menuOptionsLabel !}

    Six issues of our award winning magazine and daily delivery of The Download, our newsletter of what’s important in technology and innovation.

    See details+

    What's Included

    Bimonthly home delivery and unlimited 24/7 access to MIT Technology Review’s website.

    The Download. Our daily newsletter of what's important in technology and innovation.

/
You've read all of your free articles this month. This is your last free article this month. You've read of free articles this month. or  for unlimited online access.