SudokuBoku

Samurai sudoku Five grids, 369 squares

Four corner grids each share a box with the one in the middle, and what you deduce on one side of a shared box is law on the other.

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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 stack of figures for the table

Samurai belongs on paper more than any board we serve — a solve this long deserves a pencil and an afternoon. Your browser generates each five-grid figure, proves it has one solution, and lays it out one or two to a sheet; smaller than that and the squares stop being writable.

Difficulty

Five grids, four hinges

Lay five classic grids on one canvas: a corner grid at each compass point and a fifth in the middle, rotated into their gaps so that every corner grid shares exactly one 3×3 box with the centre. Count what that leaves and the shape of the game falls out. There are 369 distinct squares, not 405, because thirty-six of them are counted by two grids at once. There are 131 houses to satisfy — five grids' worth of rows, columns and boxes, minus the four boxes that would otherwise be listed twice. And each digit needs a home 41 times, which is worth memorising before you trust the counters under the number pad: a 9 can be "finished" in three grids and still owe you eight appearances.

The whole battlefield, to scale: five ordinary grids, four tinted boxes where they interlock, and the gaps in between — which belong to nobody, take no digits, and exist only because the geometry needs somewhere to not be. Every square outside the tinted boxes plays by rules you already know.

Everything ordinary about the figure is deliberately ordinary. A corner grid is a legitimate classic grid; so is the centre. If you have never met the variant before, the right first impression is not "a new kind of sudoku" but "five old ones, hinged" — and the whole art of the thing lives in those four hinges.

The box that answers to twelve lines

A normal 3×3 box is crossed by three rows and three columns, and that is the entire world it answers to. A shared box is crossed by three rows and three columns from each of its two grids — twelve lines, no two of which run the same squares, because the top-left grid's rows stop at its own border and the centre's carry on past it. Squares inside a shared box feel the difference directly: an ordinary samurai square watches 20 peers, exactly as it would on a lone board, while a shared square watches 32. Select one on the board above and the highlight spills into both grids at once — that sprawl is the variant, drawn live.

One shared box, amber, and every line that polices it, indigo: three rows and three columns arriving from the top-left grid, three rows and three columns arriving from the centre. Each of the box's nine squares must satisfy four lines and the box — thirteen houses touch it in all, against seven for any ordinary box.

Twelve lines squeezing nine squares makes the shared boxes the most informative real estate on the canvas, and it is why the standard opening advice for samurai is sound: when a grid stalls, go and stare at its bridge. The digits already sitting in a shared box were paid for twice, and they constrain in both directions.

Ink travels, pencil marks don't

Here is the mechanic that makes a 369-square solve feel different from five 81-square ones, and it is a distinction between kinds of knowledge. A digit you write in a shared square is simply there — the top-left grid and the centre both see it the moment the pencil lifts, no cleverness required. But an elimination you reason out is private. Suppose the top-left grid's rows have whittled a shared square down to an 8 or a 9. The centre grid cannot see those rows; by its own lights the square still takes anything. Nothing in the centre's logic will ever recover what you learned next door — unless you carry it over by hand.

A shared square is one square wearing two addresses, and only written digits cross the bridge on their own.

The hint button calls that carrying move the overlap relay, and treats it as a technique in its own right, on the rung between hidden singles and the pencil-mark patterns. That is a deliberate act of honesty rather than a convenience: because the engine models the relay as an explicit step, it can count how often a solve genuinely crosses a bridge — and refuse to call a figure "samurai-hard" when the answer is never. On our medium figures the relay is the hardest move in the path; from hard upward it fires alongside the subsets and wings those levels are named for, typically ten or more times in a solve.

Where the difficulty went

Grading five hinged grids produced the strangest yield curve we have measured on any board. Classic behaviour would predict difficulty rising steadily as clues are removed. Instead there is a hollow: from 165 clues all the way down to 128, roughly two digs in three still solve on singles alone. The bridges are the reason. Every clue the digger removes is being underwritten by a neighbouring grid, so simple deductions keep flowing across the hinges long after a lone 9×9 would have seized up. The spread only opens at about 120 clues — where we measured a third of digs landing medium, a sixth hard and three in ten expert — so all three upper levels dig to the same 120-clue budget and differ in which grade they will accept, while easy serves 185.

Two proofs stand guard over all of it, both demanded by this site's own rulebook before any variant ships. Every figure is verified to have exactly one solution as a whole — worth stating plainly, because the samurai puzzles this game was rebuilt from never checked, and a figure that admits two fillings is not a puzzle. And every figure must fail without its hinges: we cut the five grids apart, solve each alone, and if all five still pin down single solutions the candidate is thrown away as five puzzles in a costume. At the easy target about one dig in five fails that test and is discarded; below 165 clues, none do. One refusal follows the same logic in miniature — the unique-rectangle argument is never offered here, because a rectangle with a corner in a shared box answers to a second grid that can break the "second solution" the argument depends on.

Advice for a long campaign

A samurai figure is less difficult than it is long — our expert band asks nothing a single-grid expert wouldn't, just five boards' worth of it with couriering in between — so the useful skills are a marathoner's. Work one grid until it stops giving, note which bridge stalled you, and move to the grid on the far side of it; the answer to your blockage is usually being assembled over there. Trust the digit counters for pacing rather than placement: forty-one homes per digit means "37 placed" tells you how deep in the campaign you are, not where to look next. And if you print a figure from the panel above, leave the screen's biggest advantage behind knowingly — paper won't flag a wrong digit, and one error inside a shared box quietly poisons two grids at once. The share button, for what it's worth, carries all 369 squares in the link itself, and the receiving page re-proves the whole figure unique before it lets anyone waste an evening on it.