One solution, guaranteed

Crowns is a grid split into coloured regions. You place one crown in every row, every column and every region, and no two crowns may touch, not even at a corner. A fair board has exactly one answer.

With two answers, the last moves stop being logic and become a guess. Every board here, including the daily one, is built so that never happens.

Random regions almost never work

On an 8×8 grid there are 5,242 ways to place eight crowns so that every row and column has one and none touch. The regions have to cut that list down to one.

Eight random regions usually leave several of those placements standing, and sometimes none. The bigger the board, the less likely a random cut lands on exactly one.

Start from the answer

So the generator works backwards. It first picks a random answer that already follows the row, column and touching rules. Each crown seeds its own region, and the regions grow outwards by flood fill, one cell at a time, until they cover the grid.

Every region is then one connected piece holding exactly one of the answer’s crowns, so the answer is always a solution. Flood fill cannot promise it is the only one.

Then break every other answer

A backtracking solver then searches the board row by row for other solutions, collecting up to six at a time. Each one puts at least one crown on a cell outside the real answer.

The generator moves one such cell into a neighbouring region. That always kills the alternative: its old region loses the crown the alternative needed, or its new region now holds two of the alternative’s crowns. The real answer’s crowns never move, so the real answer survives every edit. The region giving up the cell only has to stay in one piece.

Repeat until the search comes back empty; the planted answer is then the only solution. A move can open a new alternative elsewhere, so the count does not always fall steadily. After 240 rounds, or with no legal moves left, the generator discards the regions and grows new ones.

Difficulty is region size

Before growing, each region gets a target size, and one setting controls how uneven those targets are. A wide spread leaves several tiny regions. A region of one or two cells pins its crown almost at once, and that crown clears its row, column and neighbours, so the board falls to simple steps. A narrow spread makes regions of similar size that interlock, and the deductions get longer.

To grade a board, a second solver plays the way a person does. It uses the simplest technique that makes progress and only escalates when stuck: the last free cell in a row, column or region first, then a region that fits in a single line, then arguments about groups of lines and about cells that every remaining option would touch. The hardest technique it needs is the difficulty. If the grade misses the target, the generator adjusts the spread and tries again.

Play today’s board or the full app. Source: the puzzle engine.