I think of myself as someone who likes Sudoku puzzles. But that’s not really true. I *never* sit at home solving these puzzles. Instead, I do them when I am somewhere else where I don’t have the ability to concentrate on anything. I can solve a Sudoku puzzle 5 seconds at a time. Compare that with reading a newspaper, which I can’t do at that level of interruption. I probably shouldn’t say it, but if I’m doing Sudoku around you, it doesn’t speak well of my keenness to be around at that moment. And this may explain why I don’t do *really* hard puzzles.

Most Sudoku puzzles can be done purely deductively. That is to say that simply by looking at the numbers, you can directly deduce what some empty boxes must be. When I first started solving these puzzles, I found that there were harder puzzles where only a couple of empty cells could be filled in. Eventually, people learn that they can solve these puzzles by going one or two steps deep: since these cells can’t contain the number 5, that means these other cells *must* contain the number 5, and that means some other cell must be the number 3 — or whatever. That might sound complex, but it’s really very easy.

## Difficult Sudoku Puzzles

Where things get difficult is where you really have no choice but to guess. Once you guess, you move forward deductively until you uncover an inconsistency or you finish the puzzle. Of course, most of the time, it is worse than that. After making a guess and trying one path, you may be forced to make a guess on that path — and maybe one after that. This is a complete pain. But there is an obvious way to use this method. Start doing the puzzle with a pen and then switch to a pencil for your first guess.

Now if you are lucky and your guess is wrong, you can then erase everything and fill in the non-guess with pen. Then you can continue on from there. But what about if you run into double or triple guesses? Colored pencils? They don’t erase well. And I don’t keep any around anyway. I only use pens. But I came upon a simple computer solution the other day, that works really well.

## An Easy Solution

I was reading, Sudoku Meaning on Labor Day 2016. For that article, I used an unsolved Sudoku puzzle for the image. It occurred to me that I really should have solved it (it’s a very easy one). So I brought the image into Paint.NET. I added a layer and entered the solution in red. A thought occurred to me: if I needed to do any guessing, I could just create another image layer and change the ink color (though it is not strictly necessary).

Of course, I will never do this. I don’t have a computer in front of me when I am playing Sudoku. But if I ever decide to tackle the “Beware! Very Challenging” puzzles in Will Shortz’s *The Little Black Book of Sudoku*, that may be the way to go. And yes: of course the book was a Christmas gift. I would never buy such a book for myself.

## Afterword

Note: I’m sure there are programs written just to help people solve Sudoku puzzles. Of course, I could just write a program that simply solved Sudoku puzzles. It’s a question of how much help you want to get.

Is what is known in the UK as ‘Killer Sudoku’ popular in the USA? It involves an actual bit of arithmetic, rather than the “fill in sets of 9 symbols” that normal Sudoku is about. Rather than getting any numbers in the solution to start with, the whole grid is divided into groups of contiguous numbers (with random shapes, each containing up to 9 numbers, but normally just a few), and you’re told the sum of the members of the group. No number appears more than once in a group, and the rest of the Sudoku rules apply.

The Guardian publishes a couple a week: https://www.theguardian.com/lifeandstyle/series/killer-sudoku

There are various tactics you can use (eg a group of 3 adding up to 7 must be 1,2, and 4, or looking for a row, column or 3×3 square that is made up from groups but either missing one number or with an extra one, and then using the difference from 45 to see what it is). But since I’ve never looked for “here’s a complete guide to how to solve Killer Sudoku”, I never know if I’ve thought of all the worthwhile ones, or am missing something obvious that would make a puzzle a lot easier to do. But looking for some definitive guide feels like cheating.

And what I do when you can’t fill in a number straight away is write all the candidate numbers, very small, in the corners of a square, and cross out ones that later become impossible.