Lemma › Techniques › Working Backwards
Olympiad problem-solving technique
Working Backwards
Start at the end. The end knows more.
In games: label the terminal position, then reason backwards — a position is losing exactly when every move from it hands the opponent a win. The winning strategy simply reads off the labels.
In construction problems: assume the object exists and deduce its properties until the construction becomes forced. Analysis first, synthesis second — the geometers' oldest trick.
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Working Backwards unlocks at Level 2 of Lemma's eight-level ladder, with lessons that teach it and drills that make it stick. 78 lessons, 624 curated problems and unlimited generated practice at six difficulties. Free to start — no card, no trial clock.
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