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MATH / The grid below contains the 16 points whose x- and y-coordinates are in the set {0,1,2,3}: [asy] size(2.5cm); for(int i=0; i<4; i+=1) for(int j=0; j<4; j+=1) dot((i,j)); ; ; [/asy]…

Problem

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problem

The grid below contains the 1616 points whose xx- and yy-coordinates are in the set {0,1,2,3}\{0,1,2,3\}: [asy] size(2.5cm); for(int i=0; i<4; i+=1) { for(int j=0; j<4; j+=1) { dot((i,j)); }; }; [/asy] A square with all four of its vertices among these 1616 points has area AA. What is the sum of all possible values of AA?
Plain-text mathematical notation (without MathML)
The grid below contains the 16 points whose x- and y-coordinates are in the set {0,1,2,3}: [asy]
size(2.5cm);
for(int i=0; i<4; i+=1) { for(int j=0; j<4; j+=1) { dot((i,j)); }; };
[/asy] A square with all four of its vertices among these 16 points has area A. What is the sum of all possible values of A?
Original LaTeX notation
The grid below contains the $16$ points whose $x$- and $y$-coordinates are in the set $\{0,1,2,3\}$: [asy]
size(2.5cm);
for(int i=0; i<4; i+=1) { for(int j=0; j<4; j+=1) { dot((i,j)); }; };
[/asy] A square with all four of its vertices among these $16$ points has area $A$. What is the sum of all possible values of $A$?

level

Level 5

type

Geometry

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Source and history

task_id
86fc2c65-5c98-54f3-866c-fd8f5101f23c
task_key
geometry--test--86fc2c65-5c98-54f3-866c-fd8f5101f23c
task_revision_id
1
config / split
geometry / test

Official source

initial import