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. 125 lessons, 1206 curated problems and unlimited generated practice at six difficulties. Free to start, no card, and every paid plan opens with 3 free days.
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