Falling Down the Sudoku Rabbit Hole

Within my last Month in Review, I noted how I’d shown my wife Nurikabe World. The reason for this was simple: she likes Sudoku, and I thought the 2 games were similar enough to where she’d also enjoy playing Nurikabe World.

Unfortunately, Mir took issue with that comparison, saying that it (Nurikabe World) looked more like Minesweeper. In my mind, this was a potato-potahto kind of situation, and I even went on to write as much in the article saying, “those are 2 sides of the same coin.” The insinuation there being that the games in question were similar enough to be lumped together even if the particulars were different.

But are they really?

Mir’s a smart lady. It’s one of her best qualities. If she felt strongly enough to tell me off for conflating Sudoku, and Nurikabe then there had to be something more to investigate.

As such, I decided to do a little digging into Sudoku, which is something I only had a vague familiarity with beforehand. That is, I knew it involved a grid, and some numbers but I hadn’t invested much thought into it otherwise. In a lot of ways, it’s not unlike my understanding of Chess: I know how all the pieces move, and what the goal is, but don’t ask me to play a serious game as I won’t have any idea what I’m doing.

Either way, I decided to try one of the boards over on The New York Times since they have a daily Sudoku puzzle.

While I can’t show you the exact puzzle that I solved, since they rotate daily, I can show you today’s easy puzzle. This’ll give you a fairly good idea of what I was looking at:

If you have even a passing familiarity with Sudoku then you can probably solve this board relatively quickly. You’ve been given almost half of the numbers already, so filling in the remainder is mostly a test of your ability to follow Sudoku’s 3 basic rules.

If you’re not familiar with those aforementioned rules, they are as follows:

• Every 3 x 3 square needs to have digits from 1 to 9 filled in
• Every line needs to have digits from 1 to 9 filled in
• There can be no repeat digits within a square, nor a line

That’ll give you a solved puzzle board in relatively short order. You can usually deduce the correct digit for a given space by simply looking at what’s around it. For example, the square highlighted in the picture above is a 3. You can determine this because the square already contains 1, 2, 4, 7, and 9, and the remaining digits (5, 6, and 8) all intersect with said square. Ergo, it is a 3 because 3 is the only available digit following Sudoku’s no repeating digits rule.

And, to be clear, you can solve the entire puzzle like this. Easy Sudoku puzzles give players more than enough filled in spaces to solve the entire board without having to do any mental gymnastics. It’s simply a matter of doing some basic process of elimination, and the whole thing will be completed.

However, the fact that there were 2 other puzzle difficulties on NYT wasn’t lost on me. I’d managed to finish my first Sudoku in around 10 minutes, and found it quite pleasant. Heck, I had to exert myself waaaaaaay harder to solve most of the puzzles in Nurikabe World. 

As such, I decided to try medium as well. How hard could it possibly be?

Oh god.

What the hell is this? I’ve been looking at this shit for 10 minutes, and have only managed to fill in 6 spaces.

What kind of terrible alternate dimension have I subjected myself to?

I don’t have that original medium board for the same reason I don’t have the original easy board, but I do remember that it took me around 98 minutes to finish it. The entire time, Miranda could hear me muttering to myself from the other room as I was trying to work out whether or not a particular square was a 6, or a 9. And don’t even get me started on those bastard 4s.

Though, I’d be lying if I said that spending 98 minutes on a Sudoku board didn’t make it extremely satisfying to eventually crack. Mir was also pleased that I’d stuck with it instead of giving up, and concluding this entire experiment a farce.

However, I did have several questions after finishing that first medium board. Namely about what kinds of strategies are employed by more experienced players when solving puzzles where the player is given fewer starting numbers.

To that end, I began by watching this Youtube video, which broke down some gameplay tips that more advanced players use while solving non-trivial puzzles.

I think the 2 tips that resonated with me best were to leverage information about the current square, and surrounding lines. You’ll notice that I already did that in my earlier example, but you can stretch that logic a lot further when solving more advanced boards.

For example, in the following board, I know that this square is a 1 based on the surrounding numbers:

I came to that conclusion as follows: I know for the third row, I still need to fill in 1, 2, 5, and 6. The open space in the 8th column (the highlight space) can’t be 2, or 5 because the 8th column already contains a 2, and 5. Ergo, that leaves 1 and 6 as the remaining candidates.

From here, we can actually remove 6 as a candidate by looking at square 6 (middle-right), and 7 (bottom left). Both of these squares contain a 6 already, and limit the potential locations for a 6 in the 9th square (bottom right). In fact, those restrictions force a 6 to appear in either of the bottom 2 spaces of the 8th column. For our purposes, this effectively acts like a filled-in 6 since I now know I need 1 of those 2 spaces to be a 6 at some point later in the puzzle. As such, we can safely declare the highlighted space as a 1 because 6 is no longer a valid option.

Logical leaps like the one I highlighted above are required to solve puzzles where you’re given fewer than 30 numbers to start with, and sit at the heart of what makes Sudoku so damn compelling. Mir even taught me a few additional tricks, which have helped me to complete several hard boards on both The New York Times, and Los Angeles Times. Better yet, my completion time is usually around 40 minutes, so it doesn’t even take half as long as that first medium puzzle on NYT did.

Obviously, I’ve been having a lot of fun solving Sudoku over the past few weeks, but I’d like to circle back to what originally prompted my investigation: is Sudoku actually different from Nurikabe (or Minesweeper)? 

Yes, and no. 

It’d be disingenuous to say that I think both games are as similar as I assumed when I first began this journey, but there’s no denying that Nurikabe and Sudoku are both logic puzzles. That’s where the similarities end though. The actual mechanics to solving Sudoku is completely different from Nurikabe, and I’ve had a lot of fun learning and improving those skills. Heck, the fact that I can even finish hard Sudoku puzzles in a reasonable amount of time now feels like a miracle after my experience with that first medium difficulty puzzle.

If this has somehow convinced you to give Sudoku a try, I can recommend the puzzles on both NYT, and LA Times. I prefer LA Times because you get access to the older puzzles and an additional difficulty that eclipses anything on NYT, but NYT’s interface is more user-friendly.

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