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Problem
![[asy] unitsize(6mm); draw(unitcircle); filldraw((0,1)--(1,2)--(3,0)--(1,-2)--(0,-1)--(-1,-2)--(-3,0)--(-1,2)--cycle,lightgray,black); filldraw(unitcircle,white,black); [/asy]](http://latex.artofproblemsolving.com/f/f/3/ff3f7c00e1a1162a19e43dda58d4387172fd8380.png)
![[asy]draw((0,0)--(0,2)--(2,2)--(2,0)--cycle); draw((1,0){up}..{left}(0,1)); dot((1,0)); dot((0,1)); draw((0,1){right}..{up}(1,2)); dot((1,2)); draw((1,2){down}..{right}(2,1)); dot((2,1)); draw((2,1){left}..{down}(1,0)); [/asy]](http://latex.artofproblemsolving.com/7/9/b/79b8d7b912a8c2771df92bb54c1c802b2bae5c0e.png)
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