Make advanced logic feel smaller

Read evidence, test every case, and check the exact conclusion.

Names are shortcuts for arguments

An X-Wing, XY-Wing, or chain is a reusable reasoning pattern. You do not need to memorize a silhouette first. Ask what the cells are forced to do, which possibilities remain, and which candidate fails in every case. The name comes after that argument.

For exampleIn an XY-Wing, the pivot has two possible digits. Follow what each choice forces in the wings before looking for a target.

Separate evidence from conclusion

Evidence is something you can check on the current board: complete candidate lists, a house’s only locations, or cells sharing a house. The conclusion is a placement or elimination that follows from that evidence. The practice walkthrough shows these separately so you can check the links yourself.

For example“These two cells are the only 8 locations in this column” is evidence. “Therefore at least one of them is 8” is the consequence.

Some methods have an extra assumption

Unique rectangles and BUG+1 rely on the original puzzle having exactly one solution. Having no repeated clues is not enough to prove that. Our puzzle validation counts solutions up to two and permits those hints only after uniqueness is established. A stopped search is reported as incomplete, never as proof.

For exampleA completely empty board has no repeated digits, yet has many completions. It is not a valid unique-solution practice puzzle.

Prove the target, then apply it

Look at every endpoint, wing, fin, or set that the explanation says can hold the digit. Check that the target conflicts with every relevant possibility. Apply only the candidates that this particular pattern proves. Other valid deductions might exist, but they need their own evidence.

For exampleAn XY-Wing target sees both wings. An XYZ-Wing target must also see the pivot, because the pivot itself might hold the eliminated digit.

Build understanding in small passes

On the first pass, read the reason without racing. On the second, trace the highlighted cells and say what each link guarantees. On the third, hide the answer and choose the target yourself. If a step is unclear, revisit its prerequisite or tap a vocabulary term. Practice is free, including advanced techniques.

For exampleA useful check is: “Which exact extra candidate or missing connection would make this argument stop working?”

Quick check

A detector finds no supported move before its search budget ends. What does that prove?

The puzzle requires guessing.
Only that this search did not find a supported move.
The puzzle must have more than one solution.

Show the answer

Only that this search did not find a supported move. Correct. A different technique, a longer chain, or another viewpoint may still reveal a deduction.

Try it with the interactive lessons Play an easy puzzle

Next, when you are ready: XY-Wing / Y-Wing.