How to Solve Sudoku Faster

Once you can finish a sudoku, the next thing you notice is the clock. At the same difficulty, one day takes five minutes and another takes fifteen. Where does the difference come from?

I think most of the gap between a fast day and a slow day comes not from how quickly you reason, but from where you are looking and how often you go back. This article goes through ways to cut down on both. I covered the basic techniques in How to Solve Sudoku: The First Techniques Beginners Should Learn, so here the focus is on using the techniques you already know more quickly. As before, “row” means a horizontal line, “column” a vertical one, and “box” one of the 3 × 3 blocks.

Accuracy before speed

First, a word about order. I think it is better to make your solving accurate before trying to make it fast.

Nothing loses more time in sudoku than a mistake. Place one wrong digit and the cells you fill because of it go wrong one after another, until a contradiction appears somewhere. Going back to find the cell that caused it takes many times longer than not making the mistake. If you never notice it, you do not finish at all.

So if you want faster times, start by getting to the point where you reliably finish without errors. Before placing a digit, can you say in a few words why it goes there? If not, don’t place it yet. That alone can change your slow days a great deal.

Fix the order you look in

The difference between fast and slow solvers, I think, shows up in the time spent deciding where to look next. A fixed order of looking cuts that time down.

Start with the most common digit

Start with the digit that appears most among the givens. If 7 already appears six times, only three boxes still need a 7, and the many 7s elsewhere rule out a lot of cells, so those last places are easy to pin down.

Look at three boxes at once

When looking for a digit, I think it is faster to look at three boxes side by side as a group than at one box at a time. Here I will call a group of three boxes in a row a band.

・ ・ ・ | ・ 7 ・ | ・ ・ ・
・ ・ 7 | ・ ・ ・ | ・ ・ ・
・ ・ ・ | ・ ・ ・ | ・ ・ ・

In this band, the left box has its 7 in the second row and the middle box has its 7 in the first row. Since each row holds only one 7, the right box’s 7 must go somewhere in the third row. Whenever two of the three boxes in a band contain the same digit, the third box’s copy of that digit belongs in the one remaining row. All that is left is to check which of those three cells has no 7 in its column.

The same works with three boxes stacked vertically. Three horizontal bands and three vertical ones: go through all six for each digit. With practice, you start to see at a glance which row of the third box a digit must be in.

Keep looking from the digit you just placed

After placing a digit, don’t jump straight to a new search. First look at what the digit you just placed affects.

• Look for the same digit again in the other boxes
• Check whether the row, column or box you just filled now has only one or two empty cells left

Placing a digit changes the situation around it, and the next answer is often right where things just changed. Searching on from where you placed a digit means far less eye movement than sending your eyes somewhere new each time.

Fewer pencil marks, written correctly

The more pencil marks you write, the longer a puzzle takes. To solve faster, write fewer.

I think it works best to go as far as you can without marks, and start writing only once you get stuck. Even then, start light: write a digit only when it is down to two possible cells within a box, and only in those two cells. When that stops working, write out every candidate in the boxes with the fewest empty cells.

I covered how to write and erase marks in How to Write Sudoku Pencil Marks.

When stuck, don’t stare at the same place

On slow days there is usually a stretch where you are stuck, and when stuck it is tempting to keep rereading the same box.

When that happens, switch methods. If you were looking for a cell for each digit, look for the digit for each cell instead. If you were scanning boxes, scan rows and columns. If nothing turns up, it is time for pencil marks. I collected ways to get unstuck in Stuck on a Sudoku? How to Find the Next Move.

Living with the clock

Watch the clock too closely and sudoku stops being fun. This is how I think it is best to treat your times.

Watch the average, not the best. A best time is partly a record of the day a puzzle happened to suit you. The average shows changes in your actual skill better.

Compare within one difficulty. The same person gets very different times on Easy and Hard. Compare your own records at the same difficulty.

Slow days are allowed. Everyone is slower when tired, or when a puzzle simply does not suit them. One slow time does not mean you have stopped improving.

Have days without the clock. Thinking about speed can bring more mistakes. Now and then, solve without caring about time, checking the reason for every digit, and your accuracy comes back.

Watching your records in Sudoku365

Sudoku365 is a sudoku app I make for iPhone, iPad and Android.

The game screen has a timer showing how long you have been solving. When you finish, that time goes into STATS. STATS shows, for each difficulty (Easy, Medium, Hard and Expert), Puzzles Completed, Best Time and Average Time. Best Time is your shortest finish at that difficulty. As I wrote above, looking at Average Time alongside Best Time makes changes in your skill easier to see.

Some settings matter for speed. With Hide placed number buttons on (the default), a digit’s button disappears once it appears nine times on the board, so you can see at a glance which digits remain. With Remove numbers from notes on (the default), placing a correct digit automatically clears the same digit from marks in its row, column and box. With Show incorrect numbers on (the default), a wrong digit is shown right away and counted as a mistake. You get three mistakes; go past that and the game is over.

The DAILY CHALLENGE is one puzzle a day, the same for everyone in the world. On iPhone and iPad, your time goes to a Game Center world ranking, where you can compare it with others who solved the same puzzle that day. The ranking is not available on Android.

There are 300 puzzles at each of the four difficulties, 1,200 in all. The app is free with ads, and a one-time Remove Ads purchase turns them off. I also wrote about reading your stats in Sudoku365 Tips: Streaks, Stats, and Steady Progress.

To me, solving faster is not about doing many things quickly. It is about spending less time deciding where to look and less time going back. Place digits correctly, and keep looking from where you placed them. Do that over and over, and I think the times follow on their own.