Types of logic puzzles

Fill in digits

Sudoku

Fill a 9×9 grid so that every row, every column and every 3×3 box holds the digits 1 to 9 once. Start with hidden singles: a digit with only one place left in a box. How to play Sudoku.

Killer Sudoku

A Sudoku that usually starts with no digits at all. Dotted cages cover the grid; the digits in a cage add up to the cage's number and never repeat. Start with cages that have only one combination, such as two squares adding up to 3, which must be 1 and 2. How to solve Killer Sudoku.

Kakuro

A crossword made of sums. Fill the white squares with digits 1 to 9 so that each across and down run adds up to the clue beside it, with no digit repeated in a run. Start with runs that have only one combination, such as 17 in two squares, which must be 8 and 9. How to solve Kakuro.

Shade squares

Nonograms

Shade squares so that each row and column has runs of shaded squares of the lengths its clues list, in order. The finished grid is a picture. Start with big clues in short lines: part of the block is shaded wherever it slides. How to solve nonograms.

Hitori

Shade some numbered squares so that no number repeats in any row or column. Shaded squares never touch side by side, and the unshaded squares stay connected. Start with a pattern like 3 5 3 in a line: one of the 3s must be shaded, shaded squares cannot touch, so the 5 stays unshaded.

Nurikabe

Shade squares to build one connected wall. Each number sits in an unshaded island of exactly that many squares, every island holds one number, and the wall never forms a solid 2×2 block. Start with the 1s: an island of one square, so all its neighbours are wall.

Draw lines

Slitherlink

Draw a single closed loop along the grid lines. Each number says how many of the four sides of its square the loop uses. Start with the 0s: none of their sides is used, so cross them all out.

Hashi (bridges)

Join numbered islands with straight bridges, across or down. Each island has as many bridges as its number, two islands share at most two bridges, bridges never cross, and in the end every island is connected. Start with an island that needs every bridge it can get, such as a 4 in a corner with two neighbours: double bridges to both.

Masyu

Draw one loop through the centres of squares that passes through every circle. On a black circle the loop turns and runs straight for two squares each way; on a white circle it goes straight through and turns in at least one of the squares next to it. Start with black circles on or near the edge: their lines must point away from it.

Place pieces

Light Up (Akari)

Place lights on white squares so that every white square is lit. Light runs along rows and columns until a wall stops it, and no light may shine on another. Numbered walls are the clues; in the Regional Akari variant, coloured courtyards that each hold one light take their place. Start with walls marked 4 or 0, or with single-square courtyards. Light Up rules.

Star placement puzzles

Place stars so that every row, every column and every outlined region holds the same number of stars, one or two depending on the puzzle, and no two stars touch, not even at a corner. Start with small regions: a region that lies inside one row takes that row's star.

Binary puzzles

Fill a grid with 0s and 1s. No row or column has three of the same digit in a line, every row and column has as many 0s as 1s, and no two rows or two columns are the same. Start with two equal digits side by side: the squares at either end of the pair get the other digit.

How to pick one

If you like arithmetic, the digit family is yours: Killer Sudoku and Kakuro add sums to the Sudoku habit. If you like seeing a picture appear, try nonograms. If you like the feeling of a whole board falling into place from a few forced moves, try Light Up: Nightwatch has a new Regional Akari board every night, free in your browser.