Doodle CubWhen a sudoku stops moving, it is almost never because you need to guess. A properly made puzzle has exactly one solution and can be solved by logic alone. When you are stuck, go back to the simplest techniques and apply them to every row, column and box, in order. Most "stuck" moments are a single you missed. Here are seven techniques, from the easiest to the ones that unlock harder puzzles.
You can practise all of them in Doodle Sudoku, where puzzles are graded by the hardest technique they need and hints name the technique instead of filling in a digit.
1. Naked single
A cell where only one digit is possible, because the other eight already appear in its row, column or box. Scan cell by cell in crowded areas: a cell whose row, column and box together contain eight different digits has only one answer.
2. Hidden single
A digit that can go in only one cell of a row, column or box, even if that cell has other candidates. Pick a digit, say 4, and look at one box: if every other empty cell in that box can't hold a 4 because of 4s in nearby rows and columns, the last cell must be the 4.
Hidden singles are the most common thing people miss. When stuck, go through the digits 1 to 9 and check each box for each digit.
3. Pencil marks, done properly
Write the possible digits (candidates) in small numbers in each empty cell. It feels slow, but it makes the next techniques visible. Update the marks every time you place a digit: remove that digit from the cell's row, column and box.
4. Naked pair
Two cells in the same row, column or box that both have exactly the same two candidates, say 3 and 7. Those two digits must go in those two cells, so you can remove 3 and 7 from every other cell in that unit. The same logic works for three cells sharing three candidates (a naked triple).
5. Hidden pair
Two digits that can only appear in the same two cells of a unit. Even if those cells have other candidates, they must hold those two digits, so you can erase every other candidate from them.
6. Pointing pair
If, inside a box, a digit can only go in cells that line up in one row, then that digit must sit in that box's part of the row. You can remove it from the rest of that row outside the box. Columns work the same way.
7. Box-line reduction
The reverse: if, in a row, a digit can only appear inside one box, it can't appear anywhere else in that box. Remove it from the box's other cells.
A routine for when you're stuck
- Check every digit for hidden singles in every box.
- Check the most crowded rows and columns for naked singles.
- If you haven't yet, fill in pencil marks for the whole grid.
- Look for pairs (naked, then hidden).
- Look for pointing pairs and box-line reductions.
- Still stuck? You may need advanced patterns like X-Wing. We will cover those in a later guide.
Why not just guess?
Guessing can work on easy puzzles, but on hard ones a wrong guess can run for twenty moves before it breaks, and you learn nothing. The techniques above are faster in the end and make the next puzzle easier.
In Doodle Sudoku, Warm-up puzzles need only singles, Solid needs pairs, Sharp needs pointing pairs and box-line reduction, Expert needs X-wings and triples, and Fiend needs XY-wings, colouring or swordfish. A hint tells you which technique to look for and highlights the cells, for 30 seconds on your time.