Classic olympiad problem · Combinatorics
A 5times5 grid has a token on each square. Every token must move to…
A grid has a token on each square. Every token must move to an orthogonally adjacent square. Prove this is impossible.
This is a proof problem. The answer is an argument, not a number. The solution is deliberately not posted here: reading a solution you didn't fight for teaches almost nothing. On Lemma you attempt it cold, take one of the 3 progressive hints only when genuinely stuck, then compare your proof against a full walkthrough and mark yourself with the same rubric a competition coordinator would use.
Train it on Lemma
This problem sits in the Olympiad Set: 89 proof problems (real IMO problems and the classics) with progressive hints, full walkthroughs and marking rubrics. 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.
Find your levelMore Combinatorics problems
- Ramsey, R(3,3)=6Classic (Ramsey, $R(3,3)=6$) · difficulty 4/6
- Mutilated chessboardClassic (mutilated chessboard) · difficulty 3/6
- Handshake lemmaClassic (handshake lemma) · difficulty 2/6
- All 89 problems →