Ripple Effect

Fill every room with 1 to its size — and keep equal numbers further apart than their own value.

What it is

A grid carved into rooms. Each room of size n holds the numbers 1…n, each once. The ripple rule: two copies of the number k in the same row or column must have more than k cells between them. A pair of 1s needs one cell of gap; a pair of 5s needs five.

How to play

Big numbers in small rooms are the levers: a 5 can only exist in a room of five or more cells, and two 5s in one row need serious distance. Fill single-cell rooms (always 1) first, then use the spacing rule as an eliminator — every placed number sweeps its value out of nearby cells in its row and column. Room completion and spacing alternate until the board closes.

History

Nikoli, published as Hakyuu Kouka (“ripple effect”), from the mid-1990s. Less famous than sudoku but prized among solvers for how physical the spacing rule feels — numbers radiate exclusion like ripples in water.

Purpose

The workspace’s second puzzle (after sudoku) on the shared constraint engine: rooms are AllDifferent groups, and the spacing rule is a custom propagator. Its development recorded two engine lessons — the Intersection propagator is unsound for rooms that can repeat a value across groups, and “unique” is not the same standard as “solvable by inference”, both now documented in the solver crate.

This implementation

• Spec knobs: rows, cols, max_room, difficulty.
• Generation: answer first — rooms are carved, the engine fills them, and givens are thinned while the board stays solvable by inference at the target ceiling (the ladder standard, not mere uniqueness — thinning to uniqueness alone once produced an 8×8 with a single clue).
• Guarantees: exactly one filling, reachable by inference; domains are restricted to each cell’s room size before the search begins.
• Difficulty: the hardest technique the ladder actually needed.
• Cross-check: the spacing propagator is verified against an exhaustive 3×3 enumeration.