SudokuBoku

Extreme sudoku

Puzzles where every technique on this site runs out. Some of these have no single, no pair and no pointing pair available on the opening grid.

Easy Medium Hard Expert Evil Extreme

00:00 Mistakes 0
Puzzle —
Rules
  • Fill every row, every column and every 3×3 box with the digits 1 to 9.
  • A digit can appear once in each of those — never twice.
  • There is exactly one solution, and logic alone will reach it.
  • Rows and columns each take the digits 1 to 9, once apiece.
  • The boxes are irregular shapes, drawn with the heavy outlines.
  • However a region bends, no digit repeats inside it.
  • The colour patches are cages; the small number is what a cage's digits add up to.
  • No digit repeats within a cage — nor in any row, column or 3×3 box.
  • There are no given digits: the sums alone pin down the whole grid.
  • Everything from classic applies: rows, columns and 3×3 boxes take 1 to 9.
  • The two tinted diagonals must each hold 1 to 9 exactly once as well.
  • All the classic constraints hold — rows, columns and 3×3 boxes take 1 to 9.
  • Each of the four shaded windows must also contain 1 to 9 exactly once.
  • The windows sit a step in from the corners, overlapping four boxes apiece.
  • Rows, columns and 3×3 boxes work exactly as they always have.
  • On top of that, two squares a chess knight's move apart may not hold the same digit.
  • Select a square and its knight partners are ringed with a dashed outline.
  • Every row, column and 3×3 box holds 1 to 9, exactly as in classic.
  • Along each grey path, digits strictly climb from the round bulb to the far end.
  • They don't have to be consecutive — each square just beats the one before it.
  • Rows, columns and 3×3 boxes take 1 to 9, exactly as in classic.
  • The digits along each arrow add up to the digit in the circle it comes from.
  • Digits may repeat along an arrow — as long as no row, column or box objects.
  • Fill every row, column and 3×3 box with the digits 1 to 9, as usual.
  • Between squares in the same box you'll find a sign; its point aims at the smaller digit.
  • Every comparison inside every box is shown — a hundred and eight of them.
  • The higher levels hand you fewer digits, not fewer signs. Expert gives you four.
  • Fill every row, column and 3×3 box with the digits 1 to 9, as usual.
  • A white dot between two squares means their digits differ by one.
  • A black dot means one digit is exactly double the other. 1 and 2 are both, and always show black.
  • A boundary with no dot is a clue too — those two digits are neither one apart nor double and half. Every boundary is marked or deliberately bare.
  • Expert hands you no digits at all. The dots and the gaps are the whole puzzle.
  • Fill every row, column and 3×3 box with the digits 1 to 9, as usual.
  • A square with a ring behind it holds an odd digit — 1, 3, 5, 7 or 9.
  • A square with a frame behind it holds an even one — 2, 4, 6 or 8.
  • Most squares are marked with neither, and those are genuinely unrestricted.
  • Every square switches to the fully marked board — one level, gentler than it looks, and two puzzles sharing a grid rather than one.
  • Every row, column and box holds five odd digits and four even ones — so once five squares of a house are known odd, the rest of it is even, marked or not.
  • Solve the 9×9 sudoku as usual — every row, column and box takes 1 to 9.
  • Ten ships are hidden on the same squares: one of four, two of three, three of two and four single squares.
  • Ships are straight, and no two of them touch — not even at a corner.
  • The numbers beside and below say how many ship squares each row and column holds.
  • A ship listed with digits sits on exactly those digits, in order — so the grid is your map.
  • Five 9×9 grids interlock: four corners and a centre, each corner sharing one 3×3 box with it.
  • Every grid obeys ordinary sudoku on its own — rows, columns and boxes each take 1 to 9 once.
  • A tinted box belongs to two grids at once, and only together do the five have one solution.
  • Fill every row, every column and every box with the digits 1 to 6.
  • The boxes are three squares wide and two tall.
  • Nothing repeats in any row, column or box.
  • Put 1, 2, 3 and 4 into each row, each column and each 2×2 box.
  • No digit may appear twice in any of them.
  • Every square can be worked out — no guessing needed.
Keyboard shortcuts
1–9
Place a digit, or toggle a pencil mark
Arrows
Move around the grid
N
Notes mode on or off
Backspace
Clear the square
Ctrl + Z
Undo · Ctrl + Y redo

A claim we can actually check

Everywhere else on this site, the difficulty label names the technique a puzzle requires. Here it names an absence. Every grid on this page has been run against all eighteen techniques we implement — singles, subsets, locked candidates, the fish, the wings, colouring, unique rectangles, almost locked sets — and none of them finishes it.

Some are more hostile than that. Sample the opening positions and you'll find grids with no naked single, no hidden single, no useful naked pair and no pointing pair anywhere on the board. There is no first move in the ordinary sense.

Every other level promises that a named technique will finish the grid; this one certifies that none of them can.

What remains true: there is exactly one solution, verified during selection. You are not being handed an ambiguous grid and told to pick.

Why patterns stop working

The techniques below this level all share a shape. Each finds a small, local contradiction — a digit with nowhere else to go, a set of squares that must consume a set of digits — and converts it into an elimination.

A well-made extreme puzzle is constructed so that no such local contradiction exists in the opening position. The information needed is spread thin across the grid, and no single neighbourhood carries enough of it. To get anywhere you have to combine implications that run through many squares.

Chains and forcing

The tool that survives is the chain. Take a square with two candidates and follow the consequences of one choice: if this is a 3, then that square isn't, which forces this other one, and so on. You're not committing — you're tracing.

Two things you might find at the end of the trace. The chain may return and contradict itself, which proves the starting assumption false and gives you a genuine elimination. Or two different starting assumptions may both force the same digit into the same square — in which case that placement is certain regardless of which was right.

That second form is forcing, and it's the most reliable way through these grids. It's also slow, and there's no honest way to make it fast: you're doing bookkeeping that a pattern would have done for you if a pattern existed.

Testing an assumption properly

At some point most solvers stop tracing and start testing — pick a square, commit to a digit, and play on until it works or breaks. There's nothing wrong with it, but there is a right way and a wrong way.

Choose a square with exactly two candidates, never three or more; you want a clean fork where disproving one proves the other. Pick one in a crowded region, so consequences arrive quickly and a contradiction surfaces sooner. And know your way back — on the board above, undo will walk you out of a failed line one step at a time.

What you should not do is guess in a sparse corner and grind forward for twenty placements. If the line is wrong you'll discover it a long way from home, and if it's right you won't be sure why.

Is that still solving?

Worth being honest about, because opinions differ and both are defensible.

One view: a proof by contradiction is a proof. Assuming a digit, deriving nonsense and concluding the digit was wrong is exactly the reasoning a chain performs — you're just doing it on the board instead of in your head.

The other: the pleasure of sudoku is that every step is known before you write it, and a test replaces knowing with trying. By that standard a puzzle needing one isn't a proper puzzle.

We take no position beyond labelling accurately. If you want grids that never require this, evil is as hard as we go while still guaranteeing a findable pattern at every step.

What the hint does here

It tells you the truth. When no technique applies, it says so rather than inventing a pattern, and offers a correct digit if you want one. Taking it is not failure — on some of these positions, no amount of looking will surface a step, because there isn't one to surface.