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 — 81 real competition problems with progressive hints, full walkthroughs and marking rubrics. 78 lessons, 624 curated problems and unlimited generated practice at six difficulties. Free to start — no card, no trial clock.
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 81 problems →