Hard Sudoku

Every puzzle is generated on the spot and has exactly one solution, and the generator aims for puzzles that cannot be finished with single-number logic alone.

What makes a sudoku hard?

Difficulty is about the techniques you need, not the count of givens alone. A hard puzzle typically leaves you without a single obvious number after the first few minutes. At that point you need to carry notes, look for patterns across several regions, and sometimes follow a short chain of reasoning to an elimination.

Because every puzzle has one solution, none of this requires luck. A chain of deductions always exists, even if it takes patience to find.

Start with a careful set of notes

On a hard puzzle, notes are not optional. After placing all the easy numbers, turn on Notes and fill in candidates for every empty square. Take your time and be accurate, because one missing candidate leads to a wrong deduction later. The game removes a number from related notes when you place it, which keeps the grid tidy as you go.

Do a full pass of simple eliminations before looking for anything advanced. Most hard puzzles shrink considerably once pairs and pointing pairs have done their work.

Techniques for hard sudoku

Naked and hidden subsets

Pairs, triples and sometimes quads of squares that share a small set of candidates let you clear those candidates from the rest of the region. Hidden subsets work from the other side: digits that fit only a few squares tell you which candidates those squares can drop.

Pointing and claiming

When a digit within a box is limited to one line, you can erase it from the rest of the line. When a digit within a line is limited to one box, you can erase it from the rest of the box. These two moves open up many stuck grids.

X-Wing

If a digit can appear in only two squares in each of two rows, and those squares fall in the same two columns, the digit must occupy opposite corners of that rectangle. You can then remove it from the rest of both columns. The same idea works with rows and columns swapped.

XY-Wing and chains

Three squares, each with two candidates, can link together so that one digit is eliminated from any square that sees two of them. Longer chains extend the idea, following forced either-or choices around the grid.

Controlled what-if reasoning

As a last resort, pick a square with just two candidates, assume one, and follow the consequences. If the assumption causes a contradiction, the other candidate is correct. Use Undo to retrace, and treat this as logic rather than a gamble.

Habits of strong solvers

• Scan the whole grid for each digit in turn, rather than staring at one region.
• Keep notes consistent and clean. Re-check them whenever you place a number.
• Look first for squares with only two candidates. They are the starting point for most advanced patterns.
• Take a break when you stall. A fresh look often shows an elimination you passed over.
• Use a hint to learn, not to finish. Ask yourself why the highlighted square works.

Scoring and personal bests

Hard puzzles begin with 2000 points. You lose a point per second, 50 per hint and 25 per mistake. A hint therefore costs as much as nearly a minute of steady solving, so it pays to look a little longer first. Your best score and fastest time are stored in your browser, so you can try to beat yourself.

A short note on history

Sudoku began as Number Place, published in a US puzzle magazine in 1979, before becoming a hit in Japan and then an international pastime in the early 2000s. The hardest puzzles have since become a hobby of their own, with solvers sharing techniques that were rarely needed in the early days.

Common questions