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USAJMO 2021 Question 4

USAJMO · USAJMO 2021

Question 4

Carina has three pins $A,B,C$, all at the origin of the coordinate plane. One move shifts one pin to an adjacent lattice point at distance $1$. What is the least number of moves needed for triangle $ABC$ to have area $2021$?

Proposed by Brandon Wang. Evan Chen’s third-party compilation; source discussion https://aops.com/community/p21498566. Source video https://youtu.be/9WNgDETHOlI?t=317.