Proven Sudoku
Do hard sudoku puzzles need guessing?
A well made one never does. Whether the one in front of you is well made is a different question, and it depends on who published it.
Nothing stops anyone publishing a sudoku that only a computer search can finish. It will still have one answer. It will still look like every other puzzle. So if a hard board has you picking a digit at random, the puzzle may be at fault and not you.
What counts as a guess
A guess is picking one of two digits with no reason, then seeing whether the board falls apart.
The test is simple. Could you say why, before you wrote it? If you could not, it was a guess. That holds even when the digit turns out to be right.
Working out that one of two options breaks the board, and writing the other one, is not a guess. That is a real step. The difference is whether you knew before or after.
One solution is not the same as one path
Here is the part most guides leave out.
A puzzle can have exactly one solution and still give you no next step you could work out. Being solvable by logic is a second promise, and it is not the same one:
- One solution. Only one way to fill the grid. Easy for a computer to check.
- Solved by logic. From any point, some next square can be worked out. Much harder to check, and nobody has to.
Most puzzles with one solution can also be solved by logic. Not all of them can. A publisher who only checks the first one can ship a board that needs a search, without ever knowing.
What we check before you see a board
Every board here is solved again by the same solver a player would be, using only the techniques at or below its level. A board that cannot be finished that way is thrown out and never published.
That check has been run across all 10,950 boards in the ten year run. None of them needed a guess. None needed a technique above its level. None had a second answer. How difficulty is decided sets out the method and the full table.
We can only speak for our own boards. We have not measured anyone else's and do not claim to.
What to try when you are stuck
Most stuck boards come unstuck at one of these. Work down the list in order.
- Fill in the pencil marks you skipped. A missing mark is the most common reason a board looks stuck. How to enter pencil marks covers the controls.
- Look for a digit with one square left. Take one digit. Go row by row, then column by column, then box by box. If only one square in that group can hold it, it goes there. That is a hidden single.
- Look for a square with one mark left. That is a naked single, and it is the fastest thing to scan for.
- Look for two squares in a group holding the same two digits. Those two digits belong to those two squares, so you can rub them out of every other square in the group. That is a naked pair.
- Check whether a digit in a box is stuck on one line. If every place a digit can go in a box sits in one row, it cannot go anywhere else in that row. That is pointing.
Still stuck after all five? Ask the game for a hint. It names the next real step and says which squares it uses, so you learn the move rather than just the digit. How to use a hint shows what it looks like.
How hard a board has to be before this matters
Our three daily levels stop well short of the techniques where guessing tempts people. Here is what each one actually needs, measured rather than claimed. Proven difficulty covers why we grade this way.
| Level | Hardest step it needs | Guess needed |
|---|---|---|
| Easy | Singles | Never |
| Medium | Locked candidates, or a pair | Never |
| Hard | A pair, or now and then an X-Wing | Never |
The technique library goes far past these, up to methods no person solves by hand. Those exist so the grader can prove a board never needs them.
Common questions
Is trial and error the same as guessing?
Yes, when you cannot say why first. Writing a digit to see what happens is a guess with a longer name.
Do I need a guess if a puzzle has two answers?
Yes. With two answers there is no way to tell them apart, so some point in the board has nothing to decide it. A board with two answers is broken, and no board here has one.
Why do some apps say hard and mean something else?
Because no rule says what the word means. A label is only worth anything if the publisher says how they set it. Ours is set by the hardest technique a board needs.