Sudoku

Sudoku is a logic puzzle with no arithmetic in it, which is the first thing worth saying, because the grid of numbers convinces a lot of people otherwise. The digits are just nine distinct symbols. You could play with nine colours or nine animals and nothing about the puzzle would change.

The grid is nine by nine, divided into nine three-by-three boxes. Every row, every column and every box must end up containing each digit from 1 to 9 exactly once. A proper puzzle has one solution and can be reached by reasoning alone — if you find yourself guessing, there is almost always a deduction you have missed.

Two techniques cover the vast majority of solving. The first is scanning: pick a digit, look at where it already appears, and cross off every row, column and box it rules out until a cell is the only place left for it. The second is working the cell rather than the digit — listing what could legally go in a single square and finding only one candidate survives. Between them you can finish most easy and medium puzzles without anything fancier.

Harder grids ask for pencil marks, which is what the notes mode is for. Jotting the candidates into each cell turns a puzzle you cannot hold in your head into one you can, and patterns start to surface: two cells in a box that can only hold the same two digits, for instance, lock those digits away from every other cell in that box.

The game opens on the Journey: four worlds — Notebook, Garden, Library and Night Ink — and each world is built around one technique. Notebook starts with box scanning and then the last remaining candidate, Garden adds row and column scanning, Library brings in pencil-mark elimination, and Night Ink asks for pairs. A card names the new technique the first time it matters, the first puzzles of each world are the shortest, and every puzzle is checked to be solvable with the techniques taught so far, with no guessing. Finishing a puzzle earns up to three stars. After the last hand-made Night Ink puzzle the Journey keeps going: every next puzzle is a fresh Night Ink grid, reshuffled from a late puzzle with one clue moved so it takes a little longer, and the puzzle numbers keep climbing.

Outside the Journey, Easy, Medium, Hard and Expert generate a fresh puzzle each time, and the difference between them is not how many numbers you start with so much as how deep the reasoning goes: Easy never needs more than scanning a box, while Expert always needs pencil-mark pointing and often pairs. There is also a shared Daily puzzle that is the same for everyone that day.

Tap a cell, then tap a number (or press 1–9) to fill it. A wrong digit shows in red straight away. Toggle Notes for pencil marks, use Erase, and Undo takes back your last digit or pencil mark (a mistake you undo still counts against your stars). Hint shows the next logical step and names the technique behind it — or fixes a wrong digit if there is one. The Rating chip at the top shows how many stars the puzzle is still worth. Arrow keys move the selection, Backspace erases, Z undoes, N toggles notes, and H asks for a hint. The Journey always opens on the furthest puzzle you have reached.