How Suvi grades a sudoku
Suvi grades each puzzle with a solver that uses only human techniques, easiest first. The grade is the hardest technique the puzzle needs, not the number of blanks.
| Grade | Hardest step |
|---|---|
| Easy | Naked and hidden singles |
| Medium | Naked pair, pointing or box-line |
| Hard | Hidden pair or X-wing |
| Expert | More than all of the above |
So when a medium grid stalls, you aren't missing a guess. You're missing one of the moves below.
Singles: the two moves behind every placement
A naked single is a square that can hold only one number, because the other eight already appear in its row, column or box. A hidden single is a number with only one possible home in a row, column or box, even if that square could hold other numbers.
Hidden singles are where most first moves come from. Pick a number, say 7, and visit each box in turn. The rows and columns that already contain a 7 rule out squares in that box; if only one square survives, it's the 7. Select any 7 and Suvi shades the others, which speeds this up. The number pad shows how many of each digit are left to place, so start with the digit that has fewest left.
Pencil marks that pay their way
From medium upwards you need candidates: the numbers each empty square could still hold. Switch on Pencil (or press P on a keyboard) and note them. Two habits keep it manageable:
- Mark a whole row, column or box at once, not a few squares here and there. Every technique below relies on complete marks.
- Let Suvi tidy up. When you place a number, that number's pencil marks vanish from the same row, column and box.
After every placement, look at the squares it touched. One that has dropped to a single candidate is a fresh naked single.
Naked pairs (medium)
When two squares in the same row, column or box can each hold only the same two numbers, those numbers must go in those two squares. No other square in that unit can have them.
| A | B | C | D | |
|---|---|---|---|---|
| Before | 3 7 | 3 7 | 1 3 7 | 1 7 9 |
| After | 3 7 | 3 7 | 1 | 9 |
A and B are the pair, so 3 and 7 come out of C and D. C is left with 1, a naked single, and once 1 is placed D can only be 9.
Pointing and box-line (medium)
These two moves link a box with a line.
- Pointing: inside one box, every possible square for a number lies in the same row (or column). The number must land on that stretch of the line, so remove it from the rest of that row outside the box.
- Box-line: the reverse. In one row (or column), every possible square for a number lies inside the same box. Remove that number from the box's other squares.
To spot them, read the candidates one number at a time. When a number's marks inside a box form a neat line of two or three, follow that line out of the box and see what it clears.
Hidden pairs (hard)
A hidden pair is the mirror image of a naked pair. Two numbers can each go in only the same two squares of a unit, but those squares carry other candidates too. Because the two numbers need those squares, everything else can be wiped from them.
Say that in one box, 4 and 8 appear only in two squares, marked 2 4 6 8 and 4 5 8. Strip both to 4 8. You now have a naked pair, and often a single appears nearby. Hidden pairs are easy to miss because the squares look crowded, so count where each number can go, not what each square holds.
The X-wing (hard)
Pick one number and find two rows where it has exactly two possible squares, in the same two columns. The number must sit in opposite corners of that rectangle, whichever way round, so both columns get their copy from these two rows. Remove it from every other square in both columns.
| Column 3 | Column 8 | |
|---|---|---|
| Row 2 | 5? | 5? |
| Row 7 | 5? | 5? |
| Other rows | no 5 | no 5 |
It works sideways too: two columns whose candidates share the same two rows clear those rows. X-wings hide in numbers that still have lots of marks late in the puzzle.
Expert: when the techniques run out
Suvi's expert grids are the ones its solver can't finish with everything above. Each still has exactly one solution, and there are two ways in:
- Bigger patterns. Triples (three squares whose candidates all come from the same three numbers), and the swordfish (an X-wing spread over three rows and three columns), sometimes break the deadlock.
- Test a square. Choose one with exactly two candidates, assume one of them and follow the consequences. If that leaves a number with no home, or two of the same digit in a unit, the other candidate is right.
Test in your head or in pencil, not with real numbers: a wrong number counts as a mistake even if you undo it.
If you only remember three things
- Singles first, and again after every placement.
- A hard grid always has a hidden pair or an X-wing in it. Count where numbers can go.
- Complete pencil marks are worth the minute they take.
Try them on today's medium, then today's hard sudoku. New to it? Start with easy.
Questions
- Do I ever need to guess on Suvi?
- Not on easy, medium or hard: the techniques in this guide always finish them. Expert grids need a bigger pattern or a careful test of one square, but each still has exactly one solution.
- What does the Hint button do?
- If a number on the board is wrong, it fixes that first. Otherwise it fills the next square a person could find and explains the step, so you can see which technique it used.
- Does a wrong number count if Show mistakes is off?
- Yes. Turning it off hides the red marks, but a wrong number still adds to the mistake count on your result.
Play it now
Sudoku is free on Suvi, on your phone or computer, no download. Also: Easy Sudoku · Medium Sudoku · Hard Sudoku · Expert Sudoku.