dominoes along their longer sides such that the midpoint of the longer side of one domino is a corner of the other domino. This construction yields two kinds of tetrominoes with opposite orientations. Let us call them 
-
-
can be tiled with 
prove that
satisfying![\[\begin{aligned}
\begin{cases}
a+b+c+d=0,\\
a^2+b^2+c^2+d^2=12,\\
abcd=-3.\\
\end{cases}
\end{aligned}\]](http://latex.artofproblemsolving.com/8/b/1/8b1923e0303c0aa79332ee4540ee1885a9cf3f08.png)
Y by Adventure10, Mango247
For every lattice point 
with 
non-negative integers, a square of side 
with center at the point is constructed. Compute the area of the union of all these squares.
with 
non-negative integers, a square of side 
with center at the point is constructed. Compute the area of the union of all these squares.
