Some puzzles ask you to know things: a word, a date, a capital city. Logic puzzles ask for nothing except attention. Every fact you need is printed on the grid, and the answer is waiting to be reasoned out, one certain step after another. There is no luck, no time pressure unless you want it, and no need to guess. When the last square falls into place, the satisfaction is entirely your own.

Sudoku is the famous one, but it is only the front door. Behind it is a whole house of puzzles, many of them developed or popularised by Japanese puzzle magazines from the 1980s onward. Each has a single neat idea at its heart. Here are seven worth knowing, with the rules and one opening trick for each.

Nonograms: pictures from numbers

Nonograms, which appeared in Japan in the late 1980s and are also called griddlers or paint by numbers, hide a picture in a grid. The numbers beside each row and above each column tell you the lengths of the runs of filled squares in that line, in order. A clue of 3 1 means a run of three filled squares, then at least one gap, then a single filled square. Work out which squares must be filled and which must be empty, and the picture appears.

The opening trick is the overlap. In a row of ten squares with a clue of 7, slide the run as far left as it can go and as far right as it can go. The squares covered in both positions, here the middle four, must be filled. Our Picture Cross offers grids from a quick five by five up to fifteen by fifteen, and three mistakes ends a puzzle, so mark squares you know are empty as you go.

Kakuro: the crossword made of sums

Kakuro looks like a crossword, but every entry is a number. Each run of white squares has a clue showing the total it must add up to, and you fill it with digits from 1 to 9 with no digit repeated inside a run. Runs cross each other, so every square must satisfy both its across and its down clue.

The trick is learning the combinations that can only be made one way. Two squares totalling 3 must be 1 and 2; two totalling 4 must be 1 and 3; two totalling 16 must be 7 and 9; two totalling 17 must be 8 and 9. Three squares totalling 6 must be 1, 2 and 3, and three totalling 24 must be 7, 8 and 9. Start with these locked runs and see where they cross. Our Kakuro is solvable by deduction alone.

Slitherlink: one single loop

Slitherlink gives you a grid of dots with some numbers inside the squares. You draw lines between neighbouring dots to make one continuous loop that never crosses itself or branches. Each number tells you how many of the four sides of its square are part of the loop. Squares with no number can have any amount.

Start with the zeros: none of their sides can be used, so mark them all as empty. A 3 next to a 0 is a gift, because the side they share is empty and the 3’s other three sides must be filled. A 3 in a corner of the grid must use both outer sides. From there, remember the golden rule: every dot has either zero or two lines touching it, never one or three. Our Slitherlink lets you mark a side as empty with a second tap, which helps enormously.

Bridges: joining the islands

In Bridges, also known by its Japanese name Hashi, circled numbers are islands. Each island needs exactly that many bridges. Bridges run straight horizontally or vertically, never cross each other, and at most two can join the same pair of islands. When you finish, every island must be connected into a single network.

The opening trick is to look for islands that have no choice. An island with a 4 in a corner, with only two neighbours, must have double bridges to both. An island showing 8 in the open must have double bridges in all four directions. Islands with a 1 next to another 1 cannot join to each other, since that would leave them cut off from everyone else.

Nurikabe: islands in the sea

Nurikabe flips Bridges on its head. Each number marks an island of exactly that many white squares. Everything else must be shaded as sea, and the sea must form one connected region. Islands may not touch each other side to side, and nowhere may the sea form a solid two by two block.

Begin with squares sitting between two different numbers. If a square touches two numbered squares, it cannot belong to both islands, so it must be sea. Islands of size 1 are already complete, so all their neighbours are sea too. Then keep an eye on two by two areas: if three squares of a block are sea, the fourth must be island.

Light Up: no bulb shines on another

Light Up, also called Akari, gives you a grid of white squares and black walls. You place light bulbs on white squares. Each bulb lights its own square and shines along its row and column until a wall stops it. Every white square must end up lit, no two bulbs may shine on each other, and a numbered wall needs exactly that many bulbs on its four sides.

A wall showing 4 is the easiest start: all four neighbours get bulbs. A 0 wall means no bulbs touch it, so mark those squares with a cross. A 3 against the edge of the grid must have bulbs on all three open sides. Our Light Up comes in seven by seven, ten by ten and twelve by twelve sizes, and each puzzle has exactly one solution.

Takuzu: just zeros and ones

Takuzu, sometimes called binary puzzles, uses only two symbols. Fill the grid with 0s and 1s so that every row and column has the same number of each, and no three identical digits sit next to each other in a line.

Two little patterns do most of the work. If two of the same digit sit side by side, the squares on either end must be the other digit: 0 0 is always flanked by 1s. If two identical digits have one gap between them, the gap must be the other digit: 1 then blank then 1 means the blank is 0. Once a row has its full quota of one digit, the rest are the other.

Why logic puzzles are so satisfying

Each of these puzzles has the same rhythm. At first the grid looks impossible. Then you find one certain square, which leads to another, and soon the solution unfolds steadily. There is real comfort in that. Life is full of problems without clear answers; a logic puzzle promises that if you look carefully enough, the answer is always there.

They are also very companionable. Two people can work on one grid together, one spotting patterns while the other checks the rules, and a grandparent who loves Sudoku can pass on the habit of patient reasoning to a grandchild in an afternoon.

Tips for any logic puzzle

  • Start with the extremes. The biggest numbers, smallest numbers and corners usually carry the most information.
  • Mark what you rule out, not just what you know. Crosses and dots for empty squares are just as useful as filled ones.
  • Never guess. If you are stuck, read each rule again and ask which one you have not used yet.
  • Start small. A small grid teaches the techniques you will need on large ones.
  • Take your time. These are puzzles to savour, not race.