Unique is not the same as fair
A puzzle has a unique solution when exactly one way of filling it obeys every rule. For a solver that means every deduction from the rules is safe, and two equally good options always mean a clue or rule you have not used yet. A puzzle with two solutions forces a coin toss somewhere.
But a unique puzzle can still be unfair. Some grids have one answer, yet the only way to find it is to try a square, follow the consequences for dozens of moves and back out if they fail. A person calls that guessing. So we check two separate things for every puzzle: that it has exactly one solution, and that a solver using only the ideas we describe on our how-to pages can reach that solution.
Two solvers for every game
Each game has two pieces of solving code in one shared module, used by the server, the web page and the generator alike, so the rules cannot drift apart.
- An exact counter. It searches every possible answer and stops as soon as it has found two. If it finds exactly one, the puzzle is unique. It prunes hard (Sown's counter works row by row and abandons a branch as soon as a column or plot can no longer get its seeds; Bimble's abandons a walk as soon as any unvisited square has fewer than two ways in, or the unvisited part of the field splits in two), but it is still a complete search, not a shortcut.
- A technique solver. It solves the puzzle the way a person would, always choosing the easiest idea that makes progress, and keeps a record of which ideas it needed and how often. That record decides the puzzle's level, and the same solver writes the hints you see in the game.
Build the answer first, then the clues
All four generators work backwards. They make a random finished answer that obeys the rules, then decide what to show you, checking with both solvers as they go. Each daily puzzle comes from a seed made from its date, so the same date always produces the same puzzle.
Sown
The generator places seeds first: one per row and column (two on twin days), none touching. It then grows a plot outwards from each seed until the garden is full. On twin days it grows twenty small patches and pairs neighbouring ones into ten plots. A garden made this way usually has more than one solution, so the exact counter finds a rival solution and the generator moves one border square of a plot into its neighbour, never a square holding one of the real seeds, then counts again. It repeats this until the real seeds are the only answer, or gives up and starts again. Every plot must be one connected piece and a sensible size. Finally the technique solver rates the garden, and it is kept only if it matches the day's level exactly.
Twill
The generator weaves a random finished swatch (with no repeated rows or columns on Sundays), adds a few ties and crosses between neighbours, then starts with every square woven. It takes woven squares away one at a time in random order. A removal stays only if the counter still finds one weave and the technique solver can still finish it within the day's limits. When a square cannot go, it tries swapping it for a tie or cross to a neighbour. At the end it drops any tie or cross that is no longer needed, and the finished swatch must rate at exactly the day's level.
Bimble
The generator starts from a simple zigzag walk through every square and scrambles it with well over a thousand small random changes, each of which leaves a valid walk. Hedges only go between squares the walk does not join, stiles only where it goes straight and oaks only where it turns. It begins with stones on most of the squares along the walk, removes them one at a time while the walk stays the only one and the technique solver can still finish within the level's limits, then removes every stile and oak the field can do without. Again, the finished field must rate at the day's level.
Nosy
The generator picks a random arrangement of suspects, places and items (and times on Sunday), then writes every true clue it can about it. It adds those clues in random order until the exact counter finds only one arrangement, then tries removing each clue again and drops any the case does not need. The finished case must include an either/or clue and a trail or time clue, must have a clue count that suits its size, and must be solved by the deduction pass. As a last check, every single clue is removed in turn to confirm that the case would no longer be unique without it.
What counts as not guessing
The games differ, so here is exactly what each allows.
- Sown: no daily garden is published if the technique solver needs its last-resort "what if" trial. Every garden falls to the four named ideas: the last free square, a squeezed plot, a starving square, and groups of plots (or twin-day boxes).
- Nosy: the deduction pass has no trial step at all. It applies one clue at a time, removing arrangements that cannot fit, and a case is only published if that alone finishes it.
- Twill: Easy and Medium swatches need no trial. Hard and Sunday swatches may need up to two short what-ifs, each at most five moves long, and those moves may only use pairs, gaps, ties, crosses and counting.
- Bimble: Easy fields need no trial and Medium fields at most one. Hard and Ramble fields need at least one by design, capped at four per Hard field and six per Ramble, each resolved within 18 or 20 deductions.
Why allow what-ifs at all? Because a short, bounded what-if is not a guess. A guess is committing to a square without knowing. A what-if is a small proof by contradiction: suppose this square is light, follow a handful of forced moves, watch a rule break, and conclude it must be dark. You never commit to anything that might be wrong, and the caps keep the chains short enough to follow in your head.
Checked again before it reaches you
When the daily files are built, each puzzle goes through a second check: the exact counter runs again to confirm the stored answer is the only one, and the solver runs again to confirm the puzzle still solves without guessing (and, for the three grid games, still rates at its level). If anything has drifted, the build stops. The same thing happens a third time when we publish a finished puzzle's answer page: the page is worked out again from the public puzzle, and if the counter disagrees with the stored answer, the page is not written. Endless mode puzzles for Sown, Twill and Bimble never ship with their answers; your browser works them out with the same code.
When you finish, the server compares your grid with the stored answer, which the counter has already proved is the only one that obeys the rules. Hints come from the same technique solver, and if a mark you have made is already wrong, the hint tells you that first rather than building on a broken grid.
What this means when you are stuck
- There is always a next step that uses only the ideas on the how-to page. Re-read the list rather than guessing.
- In Nosy, every clue is needed. The clue you have used least is the most likely key.
- In Sown, a Medium always has a starving square and a Hard always has a group somewhere.
- On Hard Twill, Bimble and Sunday days, a short what-if is fair play. Keep it short, and abandon it if no rule breaks quickly.
- If you are sure of a mark and the puzzle seems to have two answers, one of your earlier marks is wrong. A hint will say which.
Quick checklist
- Exactly one answer: proved by an exact counter that stops at two.
- No guessing: solved start to finish by a technique solver using the how-to page's ideas.
- Level: set by the hardest idea that solve needed, not just the grid size.
- Every daily rechecked when the files are built, and again when its answer page is made.
See the techniques in action in our guides to Sown, Twill, Bimble and Nosy, or check any finished puzzle against its explanation in the Sown answers archive. Then play today's Sown.