SudokuBoku

Battleship sudoku Fleet and grid 9×9

A sudoku to solve and a fleet to find on the same squares — and the digits are how you find the ships.

00:00 Mistakes 0

The fleet

    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

    Fleets for the printer

    A PDF of fresh battleship puzzles. Each sheet carries its grid, the segment counts down two edges and the fleet legend underneath, because all three are clues and a sheet missing any of them cannot be solved. One or two to a page only — the legend needs the room. The answer key rings every ship on the solved grid, so the half that took longest can actually be checked.

    Difficulty

    Two puzzles, one grid

    Every other board on this site is sudoku with something added — a rule about diagonals, about cages, about knights. This one is not. It is a sudoku and a game of battleships laid over each other, and you have to finish both.

    The fleet is the standard one: a battleship of four squares, two cruisers of three, three destroyers of two and four single-square submarines. Twenty squares of the eighty-one hold a segment. Ships are straight, they run across or down, and no two of them touch — not even diagonally, at a corner. The numbers down the right-hand side and along the bottom tell you how many ship squares each row and column holds.

    A legal fleet, taken from a puzzle this page generated. Ten ships, twenty squares, none of them touching another even at a corner — which is why the empty water around each one is as much a part of the shape as the ship itself.

    The digits are the chart

    Left there, the two halves would have nothing to say to each other. You could solve the sudoku without once looking at the counts, and hunt the fleet without once looking at a digit — two puzzles that happen to be printed on top of one another. That is the version this was rebuilt from, and it is the one thing about it we changed.

    Here the fleet list gives each ship the digits it sits on, in order. A cruiser announced as reading 4-7-2 must lie on three squares reading 4, 7, 2 — so the grid you are filling in is the chart you are searching. Solve a corner of the sudoku and ships start pinning themselves down; place a ship and you have learned something about three digits.

    The sudoku is not the setting for the fleet. It is the map.

    The battleship from the same puzzle, standing in column 5 and reading 5-4-2-6 downwards. On that grid — on any solved grid, nearly always — that reading occurs in exactly one place, so the moment those four digits are known the largest ship is no longer hidden at all.

    Why a clue's strength depends on the ship

    The interesting part is how unevenly those clues bite, and it falls straight out of what a sudoku grid is. Measured across fifteen hundred generated grids, a four-square reading like 5-4-2-6 is the only one of its kind on the board 96% of the time, and never turns up in more than two places. A three-square reading is unique 79% of the time. A two-square reading is unique 12% of the time and has been found in as many as eight places at once. And a submarine's clue — a single digit — occurs in nine places, necessarily, because every digit appears nine times on a solved sudoku and that is the definition of the thing.

    So a clued battleship gives itself away completely and a clued submarine barely whispers. Generation knows this and takes the strong clues away first: the levels below strip the battleship's digits before the cruisers', the cruisers' before the destroyers', and leave the submarines' till last, because taking those away costs a solver almost nothing.

    Both halves have to be puzzles

    There is a rule on this site that a variant's extra rule must be load-bearing — strip it away and the puzzle must stop having a single answer, or the rule was decoration. That rule does not apply to this page, and it is worth being straight about why rather than quietly making an exception. It exists to catch a board that claims a rule doing no work, where a player who ignores the rule wins anyway. Nobody wins here by ignoring the fleet, because the fleet is half the task. There is nothing to catch.

    What does apply, and what is enforced, is that each half is genuinely a puzzle. The sudoku comes from the same generator every other page uses: dug against a uniqueness check and graded by replaying it with human techniques, so Hard here means what Hard means on the hard page. The fleet is put through a search that enumerates every legal placement its clues admit and counts them — the puzzle ships only if that count is one.

    That second check is not a formality. With every digit clue stripped away, the counts alone typically leave five or more legal fleets on the same grid; the clues that survive generation are what cut it to one. It is also the check the implementation this replaces did not make, in either half — and the sudoku half is where that showed. Removing digits blind to a clue target, as it did, leaves a grid with one answer 28% of the time at its easiest setting and, measured over forty grids apiece, never at the other three. Its Hard and Expert grids had hundreds of solutions each. They were not puzzles; they were grids with an answer sheet.

    Playing two games at once

    A tap has to mean two different things on this board, so there is a switch above the number pad. In the two marking modes a tap writes straight to the square rather than waiting for a number, and the keyboard reaches them too:

    • Digits — the ordinary board, where a tap selects and the pad fills.
    • Ship — S from the keyboard; a tap claims the square for the fleet.
    • Water — W; a tap rules the square out of it.

    Marking is one layer and pencil marks are another, so turning either on turns the other off — you cannot half-be in two modes.

    A ship square shows as a filled disc and water as a small ring, which is deliberate: the two are told apart by shape before colour, so they survive being looked at quickly, printed in grey, or read by someone who does not distinguish them by hue. Undo covers marks exactly as it covers digits, the mistake counter notices a ship marked on open water, and a wrong claim about the fleet costs you the same as a wrong digit. Water needs no mark to finish: a square you never claimed is not a claim.

    The hint button knows both games. It works the sudoku first, because the digits are the substrate; when the technique ladder has nothing left to say it turns to the fleet, where it will point out a row whose count is already satisfied, a row with exactly as many free squares as it still owes, or the move this variant exists for — a ship whose reading has one place left to be. Only one of those needs the grid. It is the one worth waiting for.