How to Solve Hard Sudoku: Advanced Techniques Explained
Easy sudokus can be solved by scanning alone. Harder ones need a few more techniques. These are the ones that unlock most hard puzzles, in the order you should learn them. They all depend on writing candidates, so turn on Notes mode and fill in the possible digits for each empty square first.
1. Naked singles and hidden singles (the basics)
A naked single is a square with only one possible digit. A hidden single is a digit that has only one possible square in a row, column or box. Always look for these first. After every number you place, new ones appear.
2. Pointing pairs
Look inside one 3×3 box. If a digit's only possible squares in that box all sit in the same row (or column), then that digit must be in that row inside this box. So you can remove that digit from the rest of that row outside the box.
3. Box/line reduction
This is the reverse. If, in a row (or column), a digit can only go in squares that all belong to the same box, then that digit must be in that part of the box. Remove it from every other square in that box.
4. Naked pairs and triples
If two squares in the same row, column or box both have exactly the same two candidates, for example {4, 7}, then 4 and 7 must go in those two squares. You can erase 4 and 7 from every other square in that unit. The same idea works with three squares that share three candidates.
5. Hidden pairs
If two digits can each only go in the same two squares of a unit, those squares must hold those two digits, even if they also show other candidates. Remove the other candidates from those two squares.
6. X-Wing
Find a digit that appears as a candidate exactly twice in each of two different rows, in the same two columns. The four squares form a rectangle. The digit must go in two opposite corners of the rectangle, so it can be removed from every other square in those two columns. The same trick works with columns and rows swapped.
General tips
- Update notes after every placement. On Royal Duels, placing a digit removes it from the notes of its row, column and box automatically.
- Never guess. Every daily puzzle on Royal Duels has exactly one solution that logic can reach.
- Take a break. Fresh eyes often spot the move you missed.
The daily Hard puzzle on Royal Duels is a great place to practice these. Solving it is worth 3 points.