Logic puzzle guides

Welcome to Professor Hoot’s library. Each of these logic puzzle guides explains one puzzle type: the precise rules, how to make a start, a worked example, the mistakes everyone makes once, and how the four ranks scale the challenge.

If you’re new to variant sudoku rules, start with Classic, Killer or Thermo. If you love arithmetic, try Kakuro or Calcudoku. Every puzzle is free to play, with no accounts, no ads and no tracking.

Four ranks, one idea

Every type comes in four ranks named after the life of a mathematical idea. A Lemma is a warm-up with generous clues. A Proposition needs a real idea or two. A Theorem is near-minimal, so almost every clue is load-bearing. A Conjecture strips the clues right back and expects you to think hard. There are 99,999 puzzles per rank, each with its own number, so you can replay one or share it with a friend, and every type also has a 30-puzzle collection that climbs from Lemma to Conjecture.

However hard a puzzle looks, it has exactly one solution and you can always reach it by logic alone. When you’re stuck, Professor Hoot’s hints point out the next logical step and explain why it works, so each hint leaves you a slightly better solver.

Sudoku variants

Sixteen ways to play on the familiar 9×9 grid, plus Chimera, which layers two or three of them into one puzzle. Every variant keeps the classic rule: 1 to 9 once in each row, column and box.

• Classic SudokuRows, columns and boxes, nothing else. Pure logic at its cleanest.
• Killer SudokuCages with sums instead of given digits. Partition arithmetic and the rule of 45.
• Thermo SudokuDigits strictly increase from bulb to tip. Count the cells, bound the ends.
• Arrow SudokuThe circled digit equals the sum along its arrow. Bound circles and arrows.
• Kropki SudokuWhite dots for consecutive pairs, black for a 1:2 ratio. Missing dots matter.
• XV SudokuX marks a pair summing to 10, V a pair summing to 5. Every one is shown.
• Sandwich SudokuOuter clues sum the digits trapped between the 1 and the 9.
• German WhispersNeighbours on a green line differ by at least 5. Fives are impossible there.
• Sudoku XBoth main diagonals are extra houses. Also called diagonal sudoku.
• Anti-Knight SudokuNo digit repeats a chess knight’s move away.
• Renban SudokuPurple lines hold runs of consecutive digits, in any order.
• Palindrome SudokuGrey lines read the same from either end. Twin cells share a digit.
• Between LinesEvery digit on a line sits strictly between its two circled ends.
• Little Killer SudokuOutside clues add up the diagonals their arrows point along.
• WindokuFour shaded windows are extra 3×3 houses. Also known as hyper sudoku.
• Non-Consecutive SudokuSide-by-side cells never hold consecutive digits.
• Chimera SudokuTwo or three rule sets layered into one puzzle. The daily puzzle.

Number puzzles

Latin squares and number crosswords: no 3×3 boxes, but plenty of arithmetic, inequalities and lines of sight.

• CalcudokuA Latin square with arithmetic cages: + − × ÷. Sizes 5×5 to 8×8.
• KakuroA numerical crossword: runs of distinct digits 1–9 that hit their sums.
• SkyscrapersEdge clues count the buildings you can see. Taller ones hide shorter.
• FutoshikiA Latin square with < and > signs between neighbouring cells.

Solving techniques

Once you know the rules, the techniques are what carry you through. Our in-depth guide covers singles, pointing and claiming, pairs and triples, cage arithmetic and the rule of 45, parity, line logic, Latin-square reasoning and Kakuro combination tables.

• Solving techniques: the complete guideProfessor Hoot’s lecture notes, from first scan to the hardest Conjecture.