Show that there exists a finite set
![A \subset \mathbb{R}^2](/media/m/3/5/2/352373131adc95dacfceb11b30512047.png)
such that for every
![X \in A](/media/m/8/1/5/8154dbd547b7d255e38611ada976b93e.png)
there are points
![Y_1, Y_2, \ldots, Y_{1993}](/media/m/a/c/d/acdbbcc4dd314172c70cbb0a3d07cd54.png)
in
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
such that the distance between
![X](/media/m/9/2/8/92802f174fc4967315c2d8002c426164.png)
and
![Y_i](/media/m/7/b/2/7b2f5eb8a6cf2f14bfab427ffbe769c7.png)
is equal to 1, for every
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Show that there exists a finite set $A \subset \mathbb{R}^2$ such that for every $X \in A$ there are points $Y_1, Y_2, \ldots, Y_{1993}$ in $A$ such that the distance between $X$ and $Y_i$ is equal to 1, for every $i.$