I recently read in Owen O’Shea’s book The Call of the Primes that there are 5,472,730,538 unique solutions for a 9×9 Sudoku grid.
Yes, five billion is a very big number, but these days, billions aren’t what they used to be. I mean, think about how many newspapers, magazines, and puzzle books feature Sudoku puzzles. It’s a huge amount of material every year.
So, the thought occurs to me…how long before those 5,472,730,538 unique solutions run out?
To be fair, it’s not like reaching Peak Oil or a point of no return. I’ve solved a lot of Sudoku puzzles, and never once have I felt like I was re-solving a grid I’ve seen before, even if I was. This is purely a matter of mathematical curiosity. How long would it take for us to use up every last possible 9×9 grid?
Man, where do I begin?
Well, if I’m going to talk Sudoku puzzles, it makes sense to start with our friends at Penny Dell Puzzles.
Across seventeen Sudoku titles, they publish approximately 23,236 Sudoku puzzles a year, and probably an additional 350 per year across their Crossword/Variety and Variety titles for a total of 23,586 puzzles in a calendar year.
Now, Penny Dell Puzzles is the top puzzle publisher in North America — #humblebrag — and let’s assume there are another half-dozen publishers worldwide matching their output. That gives us a ballpark of 165,100 Sudoku puzzles published worldwide.
But what about newspapers?
According to the Newspaper Association of America, there were 1,331 daily newspapers in 2014, and there were 1,450 daily newspapers in 2005, making an 8.2% decrease from a decade before. If we apply that percentage to the number of daily newspapers worldwide as of 2005, 6,580 titles, we get 6,040 daily newspapers worldwide. And although they may not ALL have a daily Sudoku, this will help cover some of the major magazines that also carry Sudoku that I’ve excluded from my ballpark calculations.
That gives us 6,040 newspapers x 365 puzzles a year for a total of 2,204,600 puzzles a year.
Now, for other publishing efforts regarding Sudoku, Amazon.com lists 20,718 results for Sudoku, and if we apply an average of 217 puzzles per title — which seems a fair approximation, based on the stats published by our friends at Penny Dell Puzzles, the fact that some books will have more puzzles, and some results will be ABOUT Sudoku and probably contain few to none actual puzzles — that’s 4,495,806 puzzles available right now in the world’s biggest bookstore. (Yes, obviously not all of them were published this year, but hey, this is meatball mathematics.)
Unfortunately, statistics on Sudoku are sketchy at best for the mobile app market, online puzzling, and downloadable puzzles through Playstation Network, Wii, and other gaming platforms, so I can’t factor those puzzles into my calculations.
But just with the numbers I’ve got here, we’re talking about 6,865,506 Sudoku puzzles worldwide. So, if each of those Sudoku puzzles is unique — which is possible, if unlikely — that barely makes a dent in our total of possible Sudoku grid layouts, which you recall is 5,472,730,538.
So, if we’re producing 6,865,506 unique Sudoku puzzles a year, it’ll take nearly 800 years to use every possible 9×9 grid! (For the folks at Penny Dell Puzzles, it would take nearly 232,033 years! So they’re in the clear. *laughs*)
I guess we won’t be running out anytime soon.
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