What Makes a Sudoku Hard? How Difficulty Is Rated
A sudoku is hard when it forces you to use advanced techniques. A puzzle you can finish with simple scanning is easy, no matter how empty it looks. A puzzle that needs an x-wing at some point is hard, even if it has plenty of givens.
That's why two "Hard" puzzles from different apps can feel completely different. There's no single standard for difficulty, and different publishers rate puzzles in different ways.
The technique ladder
Roughly in order, these are the techniques puzzles demand as they get harder:
- Scanning and hidden singles. Enough for most Easy puzzles. See How to Play Sudoku.
- Naked singles with notes. Medium puzzles start needing candidates.
- Intersections: pointing pairs and box/line reduction.
- Subsets: naked and hidden pairs and triples.
- Fish: x-wing and swordfish.
- Chains and beyond: y-wings, coloring, forcing chains. Mostly found in puzzles built for experts.
A puzzle's difficulty is set by the hardest step it requires, not by how many easy steps it has. One x-wing in an otherwise simple puzzle still makes it a hard puzzle, because without it you're stuck.
What about the number of givens?
Fewer givens tend to mean a harder puzzle, but it's a loose link. A 26-given puzzle can be easy, and a 30-given puzzle can need advanced techniques. Givens mostly affect how long a puzzle takes, not how much thinking it requires.
The floor is 17. In 2012, researchers proved by exhaustive computer search that no standard 9x9 sudoku with 16 givens has a unique solution.
How Kodiak Sudoku rates puzzles
Our puzzles come from a large rated puzzle collection, sorted into Easy, Medium, Hard and Expert by that rating. Because the source puzzles are all fairly sparse, we reveal extra givens on the easier tiers so they feel like what they say: about 40 givens on Easy, 33 on Medium and 29 on Hard. Expert puzzles are left as they are.
Revealing a correct digit never changes a puzzle's solution, so every puzzle still has exactly one answer.
Getting better at hard puzzles
- Learn techniques in order. The Technique Journey walks through 15 short lessons, from naked singles to swordfish.
- Keep notes complete and current. Most advanced techniques are invisible without them.
- When stuck, go back down the ladder. Most of the time the answer is a single or a pointing pair you missed, not a swordfish.
- Play the same level until it feels routine, then move up one.
FAQ
Does fewer givens mean a harder sudoku?
Loosely. Fewer givens usually mean a longer solve, but difficulty mostly comes from which techniques the puzzle requires.
Why does Hard feel different in every app?
There's no standard. Each publisher rates puzzles its own way, so one app's Hard can be another's Medium.
What is the minimum number of givens?
17. A 2012 computer search proved no standard 9x9 sudoku with 16 givens has a unique solution.
How do I get better at hard puzzles?
Learn the techniques in order, keep your notes complete, and when stuck, look for simpler techniques you may have missed before reaching for advanced ones.