Trial and Error
Short answer: when the grid is genuinely stuck — no single, no pair, no locked candidate, no fish, no wing, no chain, no almost-locked set — take a cell with exactly two candidates, assume one of them, and follow the cells that forces. If the grid contradicts itself, that candidate is gone and the other one is the answer. It is last on this site because it should be last in your solve.
What trial and error looks like
Every other figure on this site points at something. This one cannot, so it shows the whole candidate map instead — forty-eight empty cells with every shape they could still take. Read it as long as you like: there is no single, no pair, no triple, no locked candidate, no fish, no wing, no chain, no almost-locked set and no uniqueness argument anywhere in it. That absence is the technique's entire precondition, and it is the only thing worth checking before you assume anything.
The contradiction is six cells deep and the whole of it lands in one column. r8c6 could only ever have held circle, square or triangle, and the branch places all three of them in column 6 — circle at r5c6, square at r7c6, triangle at r9c6. Nothing is left to put there, so the assumption was wrong. Six forced cells in a single column is still short enough to check by eye, and that is what separates a move you can make at a table from a move only a computer makes.
How to use trial and error
- Prove to yourself that you are stuck. This is the step people skip, and skipping it is what gives guessing its bad name. Work the whole ladder first — singles, pairs and triples, locked candidates, the fish, the wings, the chains. Only when all of them come up empty is this the right move.
- Pick a cell with exactly two candidates. Two, not three: with two, ruling one out places the other immediately, so a dead branch is worth as much as a live one. Prefer a cell in a crowded row, column or box — the more filled cells around it, the faster the consequences pile up.
- Assume one shape and follow only what is forced. Write the assumption somewhere you can undo it, then place nothing but singles: cells with one candidate left, and shapes with one home left in a unit. No pattern hunting inside a branch — you are testing an idea, not solving the puzzle.
- Read the result and undo everything. If a cell runs out of shapes, or a shape runs out of cells in some unit, the assumption was wrong: erase the branch and place the other candidate. If instead the branch keeps going without breaking, you have learned nothing — undo it and try the other candidate, or another cell.
Keep the branch short. If a dozen forced cells go by with no contradiction, stop: you are no longer following an argument, you are hoping. A branch you cannot hold in your head is a branch you cannot check, and an uncheckable move is worse than no move at all.
Trial and error vs a forcing chain
They prove the same kind of thing and they are not the same move. A forcing chain follows both of a cell's candidates and looks for a conclusion they share, so nothing is ever written into the grid and nothing has to be undone. Trial and error commits to one branch, changes the board, and relies on you unwinding it correctly afterwards. That is why it is the last resort and not a favourite: the reasoning is sound, but the bookkeeping is where solves go wrong.
Test a branch in your own grid
Paste a position and this page checks it the way the technique demands: if anything else still works, it names that instead. If nothing does, pick a cell, assume one of its shapes, and watch what follows. Nothing is uploaded; it runs in your browser.
Frequently asked questions
Is trial and error cheating?
No. Assuming a candidate and deriving a contradiction is proof by contradiction, which is ordinary logic — the conclusion is as certain as any other elimination on this site. What people actually object to is unbounded guessing: picking a shape, playing on, and hoping. Bounding the branch and undoing it is what makes the difference.
How is this different from guessing?
A guess is kept when it does not immediately fail. A trial is undone either way: the branch is a question, and the only useful answer is "that contradicts". If you find yourself keeping a branch because nothing has gone wrong yet, you are guessing, and any mistake further on will be almost impossible to trace.
How deep should I follow a branch?
About eight forced cells is as far as most people can track by hand, and that is the limit this site's tools use. Beyond it the branch may still be wrong, but you would not have found out by looking — you would have found out by running a search, which is a different activity from solving a puzzle.
Why does this site teach it last?
Because reaching for it early hides what you have not learned yet. Almost every position where a beginner wants to guess has a hidden single or a pointing pair in it. The techniques above this page exist so that the number of grids that genuinely need a branch is very small — and on those, this is a legitimate move rather than a failure.