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Wednesday 15 August 2018

# Professor Gary McGuire Every day millions of people all over the world take on a Sudoku puzzle.

What is it that is so seductive about filling numbers into a 9-by-9 grid that causes people to forget themselves and miss their stop or let their coffee go cold.

Number and logic puzzles have been around for many years, if not centuries. Although popularised in Japan, Sudoku as we know it was first invented by an American, Howard Garns, in 1979 and became a global phenomenon in 2005.

There is something inherently satisfying about finishing off a good puzzle. It gives us a sense of achievement.

And the faster we do it, the smarter we feel. It appeals to the human competitive instinct. We have beaten it. We rose to the challenge. We won.

A good Sudoku puzzle will not be too easy, because we feel a bit cheated if we have not been challenged. A good puzzle cannot be too hard either, for then we will just get stuck and give up. Good puzzles keep us coming back for more.

Arguably the most important feature of Sudoku puzzles is that the rows, columns and boxes provide just the right amount of complexity for the average player.

The logical reasoning required to solve Sudoku is excellent practice for anyone's mental agility. It is precisely this kind of reasoning that sharpens the mind.

We learn to look for patterns, even inventing our own, and we become quicker at recognising them. These mental habits are important in mathematics, and in critical thinking of all kinds. We also learn focus, care, and attention to detail.

Along with the growing popularity of Sudoku has come increased scrutiny and competition between people to see if certain properties of the puzzle can be found.

Apart from actually solving puzzles, there are a large number of interesting questions about Sudoku that are easily stated, but require some pretty nifty mathematics to answer.

How many Sudokus are there? The number of Sudoku solution grids has been worked out by mathematicians to be 6,670,903,752,021,072,936,960 but the number of puzzles is still unknown.

How many given numbers must there be so there is only one solution? I recently solved this problem, and with my team we showed that you always need at least 17 number clues.

We devised a set of instructions, known as an algorithm, and ran it through a 'supercomputer' to search all possible Sudoku solution grids for a 16-clue puzzle with only one solution.

It would have taken over 300,000 years on one standard computer to complete the search but with our new "checker" algorithm and access to a 'high-end supercomputer', we were able to complete the search in about 12 months or 7 million computer processing hours.

Irish Independent Supplement