Difference between revisions of "2021 USAJMO Problems/Problem 4"
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Carina has three pins, labeled <math>A, B</math>, and <math>C</math>, respectively, located at the origin of the coordinate plane. In a move, Carina may move a pin to an adjacent lattice point at distance <math>1</math> away. What is the least number of moves that Carina can make in order for triangle <math>ABC</math> to have area 2021? | Carina has three pins, labeled <math>A, B</math>, and <math>C</math>, respectively, located at the origin of the coordinate plane. In a move, Carina may move a pin to an adjacent lattice point at distance <math>1</math> away. What is the least number of moves that Carina can make in order for triangle <math>ABC</math> to have area 2021? | ||
(A lattice point is a point <math>(x, y)</math> in the coordinate plane where <math>x</math> and <math>y</math> are both integers, not necessarily positive.) | (A lattice point is a point <math>(x, y)</math> in the coordinate plane where <math>x</math> and <math>y</math> are both integers, not necessarily positive.) | ||
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| + | ==Solution== | ||
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| + | ==See Also== | ||
| + | {{USAJMO newbox|year=2021|num-b=3|num-a=5}} | ||
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| + | [[Category:Olympiad Number Theory Problems]] | ||
| + | {{MAA Notice}} | ||
Revision as of 14:56, 15 April 2021
Problem
Carina has three pins, labeled 
, and 
, respectively, located at the origin of the coordinate plane. In a move, Carina may move a pin to an adjacent lattice point at distance 
away. What is the least number of moves that Carina can make in order for triangle 
to have area 2021?
(A lattice point is a point 
in the coordinate plane where 
and 
are both integers, not necessarily positive.)
Solution
See Also
| 2021 USAJMO (Problems • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All USAJMO Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
