Splitting on a cell with two options and following one of them. Done honestly, it is a proof by contradiction: if one branch breaks a rule, the other is true. Lesson: Deduce, don’t guess
Black cell
In Light Up, a wall. It blocks light, and a number on it counts the bulbs on its four sides. Lesson: How to solve Light Up
Black pearl
A Masyu clue. The loop turns on it, then runs straight through the next square on both sides. Lesson: How to solve Masyu
Bridge
In Bridges, a straight line joining two islands in the same row or column. Two islands can share one or two bridges, and bridges never cross. Lesson: How to solve Bridges
Bulb
In Light Up, a light you place in a white cell. It lights its whole row and column until a black cell stops it. Lesson: How to solve Light Up
Listing every possibility and crossing out the ones that lead to a contradiction. Lesson: Case analysis
Category
In a logic grid, one kind of thing to match, like breeds or years. Each person has exactly one item from every category. Lesson: How to solve logic grid puzzles
Clue
The numbers beside a nonogram row or above a column. They list the blocks of filled cells in that line, in order. Lesson: What a nonogram clue says
A group of unshaded Nurikabe cells joined side to side. Each holds exactly one number, and the number is its size. Lesson: How to solve Nurikabe
Isolated group
In Bridges, a set of islands that are all full and joined only to each other. It can’t reach the rest of the map, so a finished puzzle never has one. Lesson: Bridges: no island cut off
A grid where every row and every column holds each symbol exactly once. A Skyscrapers solution is a Latin square of heights; so is a sudoku without its boxes. Lesson: How to solve Skyscrapers
In Light Up, a white cell that a bulb shines on. A lit cell can’t hold a bulb, because that bulb would shine on the first one. Lesson: Light Up: counting around numbers
Logic grid
A puzzle that matches people to items from several categories using clues, solved on a grid of × and ● marks. Also called an Einstein or zebra puzzle. Lesson: How to solve logic grid puzzles
Loop
A path that ends where it started, never crossing or touching itself. Slitherlink and Masyu each ask you to draw exactly one. Lesson: How to solve Slitherlink
Two cells in one row, column or box that can only be the same two digits. Those digits can be removed from every other cell there. Lesson: Pairs: two cells, two digits
Cells a nonogram block covers wherever it sits. Push the block all the way left, then all the way right: the cells both cover are filled. Lesson: Nonograms: the overlap rule
P
Pairing
In Tents, matching each tree with the one tent that belongs to it. A tent that is paired with one tree can’t serve another. Lesson: Tents: pairing trees and tents
A 2×2 block of shaded cells in Nurikabe. The rules forbid it, so when three cells of a square are sea, the fourth is island. Lesson: Nurikabe: pools and one sea
Predicate
A property or relation, like Cube or LeftOf. It becomes a sentence when you give it names. Lesson: Sentences and truth
∀ (for every) or ∃ (there is). It says how many pieces a sentence is about. Lesson: For every
R
Reach
The cells an unfinished Nurikabe island could still grow into with the cells it has left. A cell no island can reach is sea. Lesson: Nurikabe: walls and reach
Region
One of the outlined, colored areas of a Queens or Star Battle board. Each region holds exactly as many queens or stars as each row does. Lesson: Queens as logic
Run
In Kakuro, a line of white cells across or down, from one clue cell to the next black cell or the edge. Its digits are all different and add up to its clue. Lesson: How to solve Kakuro
A puzzle where you cut the grid into rectangles. Each rectangle holds exactly one number, and the number is its area. Also called Rectangles. Lesson: How to solve Shikaku
Slack
How much room a nonogram line has to spare: its length minus the cells the blocks and the gaps between them need. Lesson: Nonograms: the overlap rule
In Star Battle, a marked square. Every row, column and region holds exactly two, and no two stars touch, not even at a corner. Lesson: How to solve Star Battle
Sum clue
In Kakuro, the number in a clue cell. Above the slash it is the total of the run to its right; below the slash, the total of the run beneath it. Lesson: How to solve Kakuro
T
Tent
In Tents, what you place. Each tent sits beside its own tree, above, below, left or right, and no two tents touch. Lesson: How to solve Tents
A table that lists every combination of true and false for the parts and shows the value of the whole. Lesson: Not, and, or
U
Unique combination
A Kakuro total that only one set of different digits can make for its length, like 16 in two cells (7 + 9) or 6 in three (1 + 2 + 3). Lesson: Kakuro: unique combinations
Unique solution
A puzzle has a unique solution when exactly one filling makes every rule true. Good puzzles are built this way, so logic alone can finish them. Lesson: Deduce, don’t guess
V
Vacuously true
True because the condition never applies, like “every dodecahedron is small” on a board with no dodecahedra. Lesson: If … then
Valid
An argument is valid when its conclusion is true in every world where all its premises are true. Lesson: Therefore: modus ponens
Visibility clue
In Skyscrapers, a number on the edge of the grid. It counts the buildings you can see looking into that row or column, where a taller building hides every shorter one behind it. Lesson: Skyscrapers: edge clues
W
White pearl
A Masyu clue. The loop goes straight through it and turns in the square just before or just after, or both. Lesson: How to solve Masyu
Witness
One piece that makes a “there is” sentence true. Lesson: There is