Off by one: the Sudoku Joburg Social

Written by David Clark

International Sudoku Day falls on 9 September (9/9, naturally), so our Sudoku Social on Thursday 10 September was, strictly speaking, off by one. For a society of operations researchers that felt about right: most of us have spent a career landing in the vicinity of the optimal. Real-world problems are sneaky like that.

It was a great get-together of new and old members. I'll take a guess and say the ages in the room spanned at least 40 years, which says something about the field: OR problems keep you young, because you can never really stand still. The tools change, the problems change, and the people who solved yesterday's version are still curious about today's.

We opened with a round of Sudoku trivia rather than Sudoku itself, no pencils required. A few highlights, starting with the history:

1. Who invented modern Sudoku, and under what name?

2. Which 18th-century mathematician's construction is the puzzle's direct ancestor?

And for the mathematically inclined:

3. How many valid completed 9x9 grids are there?

4. What is the smallest number of clues that still gives a unique solution?

5. Which constraint does the heavy lifting when a CP solver tackles Sudoku?

Answers at the bottom.

AI was the dominant theme of the evening's discussion. There is a lot of excitement, and a fair amount of concern, about the powerful models available today, and everyone in the room had opinions they were happy to share and debate. Three threads stood out.

Data transparency and governance. If models are going to inform public decisions, the data and assumptions behind them need to be open enough to be checked. This is old ground for OR; a model nobody can audit is a model nobody should trust, but the stakes are higher when the model is a black box that speaks fluently.

AI in call centres. Several ORSSA members will have had first-hand experience of assistants being deployed to support agents and customers. The upside is real; so is the risk of confidently incorrect answers, and the reputational and legal risk that brings. Balancing those is a multi-objective systems-design problem, which is to say an OR problem in AI clothing. My AI will call your AI.

And, of course, the rugby. Which turned, as it always does, into a brief diversion on sports analytics and the business of sport, another rich field for OR problems.

Thank you to everyone who came, especially those attending an ORSSA event for the first time. Debates like these are the reason the society exists: a room where practitioners, academics and students can discuss problems that interest us. If you missed this one, keep an eye on the ORSSA channels for the next social; we'll try to land on the right day.

Answers

1. Howard Garns, a retired Indianapolis architect, in 1979, as "Number Place" in Dell Pencil Puzzles & Word Games magazine.

2. Euler's Latin squares (1782), though the Korean mathematician Choi Seok-jeong published one in 1700. Sudoku is a 9x9 Latin square with added 3x3 box constraints.

3. About 6.67 x 10²¹.

4. 17, proved in 2012 by McGuire, Tugemann and Civario using a computer search of some seven million CPU-hours. Nobody seems to have complained that mathematics faced an existential crisis because of machines though.

5. AllDifferent. The human techniques we learn turn out to be weak forms of the same propagation.