4×4 sudoku Shidoku · 16 squares

The whole game, small enough to hold

Shrink sudoku as far as it will go and this is what remains: four rows, four columns, four 2×2 boxes, each needing the digits 1 to 4 exactly once. In Japanese puzzle publishing the size has its own name, shidoku, from shi, the number four. Nothing about the contract changes on the way down — one solution, reached by reasoning, no guessing — but the scale of the game collapses in a way that is worth pausing on. A standard grid admits around 6.7 sextillion completed arrangements. This one admits 288. We didn't take that number from a reference; our enumeration for this page walked every possibility and counted them.

It gets tighter. Take any completed 4×4, rename its digits, shuffle rows and columns within their bands, swap the bands, flip it across the diagonal — all moves that leave the logic untouched — and you can turn it into one of exactly two arrangements. Every grid this board will ever deal you is one of the pair below in a costume.

Every puzzle there is, graded

A puzzle is a completed grid with some squares hidden, so on this size the set of all possible puzzles is finite in a way you can actually exhaust: 288 grids, each with 65,536 ways of choosing which squares to reveal. For this build we ran the lot — 13,579,680 of those choices leave a puzzle with exactly one solution — and replayed every single one against the same ladder of human techniques that grades the other boards on this site. The result could hardly be cleaner. All of them, without a single exception, fall to the naked single: the move where a square has one digit left that its row, column and box permit. No 4×4 puzzle can require a hidden single, a pair, or anything with a grander name. The rungs above the first one simply have no work to do here.

The clue arithmetic came out just as crisply. No puzzle with three givens is unique — we tried all 35,840 of them — while four givens can be enough, and every minimal puzzle in the space carries four, five or six. That is why a fresh deal here starts with four clues whenever the dig lands one, and never more than a handful: fewer starting digits is the only meaningful sense in which one 4×4 can offer more puzzle than another.

On this board difficulty is not an estimate. Every puzzle that can exist has been checked, and they are all, provably, the same kind of easy.

This is also why the board above has no difficulty selector, alone among our boards. The 6×6 supports three honest levels and we measured our way to that number; here measurement gives way to proof, and the proof says one. Chips reading Easy, Medium and Hard over puzzles that are logically identical would be the kind of decoration this site was built to refuse.

Where a first solve should happen

What do you give someone — a child especially — who has never solved a sudoku? The usual answer is a big grid stuffed with clues, and it is the wrong answer: seventy squares of bookkeeping in which the one idea that matters appears over and over, drowned. The better gift is the smallest grid that still plays by the real rules, dealt as empty as the rules allow.

One question, sixteen times

Solving here means asking a single question of a square: which digits can it still see? Look at the top-right square in the lesson below. Along its row sits a 1, down its column sits a 3, and inside its little box sits a 2 — so a 4 is the only thing it can legally hold. Write it in, and somewhere else a square has just been squeezed down to one option of its own. The chain never breaks before the grid is full.

Notice what the starting position manages with almost nothing. An entire row and an entire column hold no clue at all, yet nothing in the grid is free. That is the lesson a 4×4 teaches better than any other board: a sudoku clue acts at a distance, through every house it belongs to — a thing that takes weeks to feel on a full grid and about three puzzles to feel here.

How to hand it over

Resist explaining. Point at any empty square and ask what's missing from its row; then, of those digits, what its column and box already own. The moment of finding a square with one survivor is the whole pleasure of the game, and it belongs to the solver, not the explainer. Mistakes take care of themselves at this scale — a wrong digit collides with a neighbour within a move or two, close enough to the error that a beginner can see why it was wrong rather than just that it was. When sixteen squares start feeling cramped, the promotion path is waiting: the same question asked politely by this grid is asked six ways at once on the six-by-six, and an easy 9×9 after that is a difference of stamina, not of idea.

Built like the big boards, sized like a toy

Small does not mean simplified. This board is the same engine and the same interface as every other on the site with the side length turned down: the number pad counts how many of each digit remain, the Hint button explains the reasoning for a square instead of blurting the answer, pencil marks arrange themselves in a 2×2 that mirrors the box, and a finished game offers to deal again at once because generation takes a millisecond. Even the share button keeps its full meaning — the link encodes the sixteen squares themselves, and the receiving page re-proves the puzzle has one solution before it will show it to anyone.

On paper the size becomes an advantage of its own. Six grids to an A4 sheet gives each square just under 16 mm, roughly double a newspaper cell; at two to a sheet the squares reach 26 mm, and a single grid fills the page with squares 44 mm across — the difference between a puzzle a six-year-old can write in and one they can only point at. Print a dozen sheets, leave the answer key on the last page, and the kitchen table has a week of quiet ahead of it.