Arithmetic takes the place of vocabulary
A crossnumber uses the familiar crossword grid, but each entry is a number rather than a word. Clues describe mathematical relationships—perhaps an entry is a multiple, a square, or the sum of two others—and the solver works out the values that fit. The answers are integers: whole numbers, including negative numbers where a puzzle allows them, rather than fractions or decimals.
The grid still gives each answer a fixed length. A three-cell entry, for example, must be a three-digit number, so the clue’s equation has to produce a value of the right size as well as the right kind.
Crossings turn answers into constraints
A number written across shares its cells with numbers written down. In a standard digit-by-digit grid, each crossing requires the two answers to use the same digit in that cell. That makes every solved entry evidence about its neighbors: a partly known number may rule out most possibilities for another clue, even before its full equation is clear.
Solving therefore moves back and forth between arithmetic and the grid. A clue narrows a number’s possible values; its digits then narrow the crossing entries; those entries may reveal a missing digit or make another equation solvable. The puzzle is not just a collection of calculations but a network of linked conditions.
Setters control the difficulty through links
A setter can make a grid tougher by choosing clues that leave several plausible values at first, then arranging crossings so that only one combination fits. The challenge comes from coordinating the clues, entry lengths, and shared digits—not from doing long arithmetic alone. A single correct value can unlock several entries, while one mistaken digit can create contradictions across the grid.
That is why a crossnumber often feels like a logic puzzle with arithmetic as its language: every answer must satisfy both its equation and the digits imposed by the surrounding grid.
