Sudoku

One answer, and the grid can prove it

Every grid here is cut out of a finished solution rather than typed in by hand. The generator fills a board, then takes clues away one at a time, and after each removal a counting solver checks what is left. If it finds a second way to complete the grid, the clue goes back in. What survives has exactly one answer.

That matters. On a grid with two solutions there is a point where two cells can be swapped and both readings are right, and you cannot reason your way out of it, only guess. Here, two candidates with nothing to choose between them means you have missed something elsewhere.

Pencil marks are a memory aid, not a to-do list

Press N and the board switches to notes. A digit now drops a small candidate into the cell instead of filling it, and pressing the same digit again takes the mark away, so a wrong mark costs one keystroke to fix.

The mistake almost everyone makes is pencilling all nine candidates into every empty cell when the grid appears. On a hard grid that is more than four hundred small digits to read past. Wait until a cell is down to two or three possibilities.

Place a digit properly and it is struck from the notes of every cell in the same row, column and box, because it can no longer go there. A hint does the same and then fills the cell.

The score is a budget, and it drains

You start a grid with the par for the difficulty already on the board: 300 on easy, 450 on medium, 600 on hard. Every cell you fill correctly that was not an original clue is worth 10, and there are 45 of those on easy, 51 on medium and 55 on hard, so the most you can finish with is 750, 960 and 1150.

Three things drain it. A wrong digit costs 20, a hint costs 40, and the clock takes a point every fifteen seconds. Two mistakes and one hint on a hard grid solved in twelve minutes leaves you near 900.

The floor is 25, because finishing is the point and an abandoned grid scores nothing. Your best is kept in this browser with the difficulty that earned it.

How to crack a hard grid without guessing

Select any cell and two things happen. Every cell in its row, column and box is shaded, and every other cell holding the same digit lights up. When most of a digit is down, select one and count the lit squares: the gaps tell you where the last few go.

Work boxes rather than rows. A digit with one possible home inside a box is a hidden single, and nine cells are easier to scan than a whole line. If a digit's candidates inside a box all sit on one row, it cannot appear anywhere else on that row, so cross it out yourself.

The right-hand column counts how many of each digit are placed. When a tile reads 8/9, the last one usually falls to elimination rather than logic.

Questions that turn up about three quarters of the way through

Can a puzzle here have more than one solution?

No. Every clue that comes out is tested against a solver that counts solutions and stops at two, and a removal is kept only if exactly one solution remains. If you are stuck in a way that feels ambiguous, you made a wrong mark earlier rather than finding a flaw in the grid.

I placed a wrong number early on. Is it worth starting again?

Usually not. A wrong digit shows up red, costs 20 once, and the same-digit highlight finds it the moment you select anything in its row or column. R wipes the grid back to its clues and resets the clock with it, so you lose every correct cell too.

Does a hint cost me more than a mistake?

Yes, twice as much: 40 against 20. That is deliberate. A mistake is something you can undo; a hint hands you a digit you would otherwise have reasoned out. Use them when one square is blocking everything behind it, not to race the clock.

Why did the score drop while I was doing nothing?

The clock takes a point every fifteen seconds, whether or not you are moving. It is slow enough that thinking is never punished, and steady enough that the number in the corner always tells the truth about how long you have been on the same grid.

Can I play the whole thing without a mouse?

Yes, and that is the intended way. Arrows move the cursor, the number row places digits, and every other control is a single letter. The grid and the strip below it take clicks as well, but nothing is hidden behind the mouse.

Why this one has no way to lose

A Sudoku you can lose is a Sudoku you will guess at. The moment a wrong digit ends a run, the sensible move is to fill the grid by trial and error and let the game tell you when you are wrong, which turns a logic puzzle into a slot machine. So there are no lives and no game over here: you can sit on a hard grid as long as you like, and a wrong number costs twenty points and a red digit.

The other half of that decision is the generator. Most browser Sudoku either ships a fixed handful of hand-made grids, or accepts whatever you type and never checks. Cutting a fresh grid every run, with a real uniqueness check behind it, was the part worth doing properly.