Astounding Sudoku Math: $27,000,000 From Sudoku

Not Solving Sudoku With Math But Some Cool Sudoku Math

If you’re like me, you cringe when you have to do any math beyond counting how many shoes you’re wear today.  So the phrase “sudoku math” may make you feel like running for the hills and I can relate.  But wait,  don’t run!  This article is not about solving sudoku with math, but rather it’s all about some pretty cool, even nerdy, math related to sudoku.

I think we can all agree that nerdy actually turns out to be pretty darned cool.  So, come along for a ride on the Great Sudoku Math Coaster!

FatMunkey’s Version Of Sudoku Math

At the time of this writing, I have published over 100 FatMunkey’s Sudoku Books.  Each one them contain 200 puzzles.  That’s a total of…wait, let me get my calculator app…20,000 sudoku puzzles.  To my weak mind, that seems like an awful lot of sudoku puzzles.  Other people should stop writing sudoku books because I have basically used up all of sudoku puzzles, right?

The Stars, Like Dust: A Mathematician’s Version Of Sudoku Math

Nope.  That’s woefully, stupendously far from correct!

There are a staggering number of possible, solvable sudoku puzzles.  Here is how many there are:

6,670,903,752,021,072,936,960

Contemplate that number.  I’ll wait.

In plain English that’s six sextillion, six hundred and seventy quintillion, nine hundred and three quadrillion, seven hundred and two trillion, twenty one billion, seventy two million, nine hundred and thirty six thousand, nine hundred and sixty possible, solvable sudoku puzzles.

I recently read an article which stated that there are between 3 and 7 X 10²² stars in the universe.  That is either somewhere between 3 and 7 with 22 zero behind it.  Like this:

60,000,000,000,000,000,000,000

So, there are more stars (by a factor of 10) than there are sudoku puzzles, but imagining all the stars in all the galaxies in all of the observable universe is a good way to visualize how many sudoku puzzles there really are.

These Are The Days Of Our Lives: Sudoku Math In Terms Of Time

Here is another way to put the number of sudoku puzzles into some understandable perspective. If every man, woman and child on Planet Earth finished ten sudoku puzzles a day, seven days a week and 365 days a year, we would not run out of sudoku puzzles for well over 230 million years.

That’s a long, long time and lot of sudoku puzzles!

But What About Duplicates?

Yes, there are duplicates.  Not all of those sudoku puzzles are unique, and many of them may be unique but still very similar to one another. Even so, there are still more than enough unique puzzles for everyone to enjoy.  Also, when you consider the wide variety of sudoku variations, such as samurai sudoku, Killer sudoku, various larger and small sudoku grid sizes and so forth…WELL!  There are far far far more sudoku puzzles that the stars in the universe.

Sudoku Math: Using Combinatorics To Narrow Down To Unique Grids

As nerdy as this may seem, let’s talk about combinatorics.  I’m no math wizard.  So if you’re reading this and you’re a math genius, please forgive the very simple way in which I will attempt to explain “sudoku math”!

Combinatorics is a field of math (not just sudoku math) that deals with problems of selection, arrangement, and operation within a finite or discrete system.

In the case of sudoku, we can use combinatorics to take any one sudoku grid and create enough unique sudoku grids for you to do one every day for the next century. By transposing and rotating the grid or interchanging columns and rows we can exponentially derive more grids from the original seed grid.

However, many of the puzzles created this way are essentially the same. The difficulty and probable starting points won’t vary drastically. Of all the unique possibilities for a Sudoku puzzle, only about 5.5 billion are actually different and can’t be derived from each other. That may seem like a smaller number, compared to six sextillion, but it’s still an incredibly large amount of puzzles.

In fact, it would take a single person over 173 years to get through all of the different puzzles, even if they finished one every second.

Returning to FatMunkey’s Version of Sudoku Math

So, getting back to what I started with in this article, under the heading of FatMunkey’s Version of Sudoku Math,  are there enough unique sudoku puzzle given that my one hundred plus published sudoku books have eaten up 20,000 sudoku grids?

Obviously, the answer is a resounding no.  I want to have a little fun here.  How many books would I need to publish to use up all of the unique sudoku grids? There are 5,472,730,538 unique sudoku grids that cannot be derived from each other.  If each of my published books contain 200 sudoku puzzles, I would need to publish 27,363,653 books to use all of them.

If I can sell just one of each of them and profit $1.00 on each, well, I’ll be set for life!

I better get to work!