How to play Samurai Sudoku

Samurai Sudoku joins five ordinary Sudoku grids into one big puzzle. Four grids sit in the corners of the board and a fifth sits in the middle, overlapping each of the others by one 3x3 corner box. Every grid follows the classic rule - each row, each column and each 3x3 box holds the digits 1 to 9 exactly once - and the four shared boxes have to satisfy two grids at the same time. That is the heart of the puzzle: a digit found in one grid often unlocks a box in its neighbour.

Every puzzle here is made fresh by the game when you start it, has exactly one solution, and can be solved by reasoning alone. You never need to guess. With 369 cells to fill, a Samurai is a long puzzle - settle in, and remember the game saves every move.

How to play on skill.games

When you open the game, the settings popup appears. Choose a level under DIFFICULTY, choose how mistakes are treated under MISTAKES, and press PLAY. The game builds a new puzzle; on a phone that can take a second or two, and "Generating a new puzzle…" shows meanwhile.

• The board is the whole Samurai: five grids in the shape of an X. The four boxes where grids overlap are lightly shaded. Digits printed in dark ink are the givens; the digits you enter appear in blue.
• On a phone: the whole board would make cells too small to tap, so the board works like a window. At first you see all five grids. Tap a grid to zoom into it - the cell you tapped is chosen at once. Zoomed in, the grid fills the window and the edge of its neighbour peeks in at the shared corner; tap a peeking cell to move straight into that grid. The first tool button, which shows a little map of the five grids with the current one filled, takes you back to the whole board (ZOOM goes back in). The arrow keys also walk from grid to grid.
• On a computer or a tablet the whole board fits with comfortable cells, and there is no zooming: just click or tap a cell.
• Choosing a cell: its row, column and box are shaded - in both grids for a cell in a shared box - and every cell holding the same digit is highlighted.
• Entering a digit: with a cell chosen, tap a number on the number pad (under the board, or beside it when your screen is wider than it is tall). The small number under each key shows how many of that digit are still to place: each digit appears 41 times on a finished board.
• NOTES: tap NOTES to switch notes on. Numbers you tap are pencilled into the cell as candidates, and tapping one again removes it. When you enter a digit, it is removed automatically from the notes of every cell that shares a row, column or box with it - in every grid it belongs to.
• ERASE clears the chosen cell. UNDO takes back your last action, all the way back to the start; it is free and unlimited.
• Highlighting a digit: with no cell chosen, tap a number on the pad to highlight every cell and note holding that digit.

On a computer you can also use the keyboard: the arrow keys (or W, A, S, D) move between cells and skip the gaps between grids, 1 to 9 enter a digit, Shift and a digit pencil a note, Backspace, Delete or 0 erase, N switches notes on and off, Z undoes, and M switches between the whole board and a zoomed grid when the screen is small.

The top line shows the clock, the level and your mistakes. The clock runs only while you play. The menu button in the top-left corner pauses the game, starts a new puzzle or switches the sound on or off. If you close the page you can press CONTINUE later and carry on with the same board, notes, clock and undo history.

When the last cell is filled correctly, the whole board ripples and the results screen shows your time, your best time at that level, your mistakes and the puzzle's code, together with your wins, losses, win rate and streaks.

Rules

The board. Five 9x9 grids: top-left, top-right, centre, bottom-left and bottom-right. The centre grid shares its four corner boxes with the four outer grids. The gaps between the outer grids are not part of the puzzle.

Each grid is a Sudoku. In each of the five grids, every row, every column and every 3x3 box must hold each digit from 1 to 9 exactly once. A row or column of one grid does not continue into another grid: the top-left grid's top row and the top-right grid's top row are separate.

Shared boxes. A cell in one of the four shaded boxes belongs to two grids at once, so its digit must fit the row and column of both. Each shared box still holds 1 to 9 once.

Givens. Some digits are placed at the start and can't be changed. Every puzzle has exactly one way to complete it.

Mistakes - Unlimited (the default). A digit that is already in the same row, column or box of any grid it belongs to is marked in red and counted. Nothing else is checked, just as on paper. The puzzle is solved when every cell is filled and nothing clashes.

Mistakes - 3 lives. Every digit is checked against the solution at once. A wrong digit costs a life; the third mistake ends the game as a loss. Undo can take a wrong digit back, but not the life it cost.

Abandoned puzzles. Starting a new puzzle before finishing the current one counts as a loss for that level.

Solving techniques

The game's solver grades every puzzle with the same methods a person uses, applied to all five grids at once.

• Hidden single: a digit that can only go in one cell of a row, column or box.
• Naked single: a cell where only one digit is still possible.
• Pointing pairs and box-line reduction: a digit confined to one row of a box can't go elsewhere on that row - and the other way round.
• Naked and hidden pairs: two cells that can only hold the same two digits claim them; two digits that can only go in the same two cells claim those cells.
• Triples, X-Wing and XY-Wing: the same ideas with three cells, a digit locked into two rows and two columns, and three two-candidate cells forcing a digit.
• Advanced: XYZ-Wing, Swordfish, quads, simple colouring and XY-Chains - longer chains of reasoning, never guessing.

Strategy tips

• Work the shared boxes. A shared box gets clues from two grids, so it is often the first place where something is forced. Fill it and both grids move on.
• Start with the easiest grid. Grids differ: one may have more givens or a friendlier pattern. Solve as far as you can there, then carry its shared box into the centre.
• Let the centre connect. The centre grid touches all four others. Digits that reach it from one corner often open the opposite one.
• Scan for singles first, notes later. On a board this size, pencilling every candidate takes a long time. Write notes for one box or row when singles run out.
• Watch the number pad. Each digit appears 41 times. A key with a small count left tells you which digit to hunt for.
• Don't guess. Every puzzle can be solved by logic. If you are stuck in one grid, look at its neighbour through the shared box.

Difficulty levels

The game generates every puzzle on the spot and grades it with a solver that always uses the easiest step available. A puzzle is given to you only if its hardest required step, anywhere on the board, matches the level you chose.

• Easy: at least half the board is filled in (185 of 369 cells); hidden and naked singles are all you need.
• Normal: at least 40% of the board is filled in (148 of 369 cells); at least one step needs a pointing pair, box-line reduction or a naked or hidden pair.
• Hard: at least 30% of the board is filled in (111 of 369 cells); at least one step needs a triple, an X-Wing or an XY-Wing.
• Crazy: at least 20% of the board is filled in (74 of 369 cells); at least one step needs simple colouring, an XY-Chain, an XYZ-Wing, a Swordfish or a quad.

Statistics and best times are kept separately for each level. A Samurai takes several times as long as a single Sudoku, so even Easy is a good session - start there if the shape is new to you.