155 birds
![P_1, \ldots, P_{155}](/media/m/4/a/0/4a08ba468aa8a34c3cf6a2d9a3e3a6f5.png)
are sitting down on the boundary of a circle
![C.](/media/m/4/6/7/467f2e8003bd034885e63601825c1836.png)
Two birds
![P_i, P_j](/media/m/b/6/4/b64a1ae1651bcb3c07a17daa8c1ea39f.png)
are mutually visible if the angle at centre
![m(\cdot)](/media/m/8/1/d/81d6a70f6c8855927d5b0d88be3c3f54.png)
of their positions
![m(P_iP_j) \leq 10^{\circ}.](/media/m/f/3/1/f3116cf5554396249bc55b4944e09873.png)
Find the smallest number of mutually visible pairs of birds, i.e. minimal set of pairs
![\{x,y\}](/media/m/3/d/9/3d95866d0ad819208a30af63b68d4e61.png)
of mutually visible pairs of birds with
![x,y \in \{P_1, \ldots, P_{155}\}.](/media/m/8/d/b/8dbfd87366a8a8fa9573caff7b2646c6.png)
One assumes that a position (point) on
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
can be occupied simultaneously by several birds, e.g. all possible birds.
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155 birds $P_1, \ldots, P_{155}$ are sitting down on the boundary of a circle $C.$ Two birds $P_i, P_j$ are mutually visible if the angle at centre $m(\cdot)$ of their positions $m(P_iP_j) \leq 10^{\circ}.$ Find the smallest number of mutually visible pairs of birds, i.e. minimal set of pairs $\{x,y\}$ of mutually visible pairs of birds with $x,y \in \{P_1, \ldots, P_{155}\}.$ One assumes that a position (point) on $C$ can be occupied simultaneously by several birds, e.g. all possible birds.