![(SWE 3)](/media/m/1/6/9/169f9a94c8a51b7077a36491a402ce74.png)
Find the natural number
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
with the following properties:
![(1)](/media/m/2/5/e/25e5e167a3616378fc4ad422677ae0c4.png)
Let
![S = \{P_1, P_2, \cdots\}](/media/m/1/2/f/12f2bd561098167c7618c9468e87cf1e.png)
be an arbitrary finite set of points in the plane, and
![r_j](/media/m/7/d/d/7dd3cb3f934b9c47e84da6137658c096.png)
the distance from
![P_j](/media/m/d/b/9/db9eb9cbdccb4b0c7d733cc89714da5f.png)
to the origin
![O.](/media/m/8/c/f/8cfaee47aa222d4f9d799d2e79461ae5.png)
We assign to each
![P_j](/media/m/d/b/9/db9eb9cbdccb4b0c7d733cc89714da5f.png)
the closed disk
![D_j](/media/m/1/6/9/169c1e7e8e89bd7c992109d162a962e3.png)
with center
![P_j](/media/m/d/b/9/db9eb9cbdccb4b0c7d733cc89714da5f.png)
and radius
![r_j](/media/m/7/d/d/7dd3cb3f934b9c47e84da6137658c096.png)
. Then some
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
of these disks contain all points of
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
is the smallest integer with the above property.
%V0
$(SWE 3)$ Find the natural number $n$ with the following properties:
$(1)$ Let $S = \{P_1, P_2, \cdots\}$ be an arbitrary finite set of points in the plane, and $r_j$ the distance from $P_j$ to the origin $O.$ We assign to each $P_j$ the closed disk $D_j$ with center $P_j$ and radius $r_j$. Then some $n$ of these disks contain all points of $S.$
$(2)$ $n$ is the smallest integer with the above property.