IMO Shortlist 1989 problem 29
Kvaliteta:
Avg: 0,0Težina:
Avg: 0,0 155 birds
are sitting down on the boundary of a circle
Two birds
are mutually visible if the angle at centre
of their positions
Find the smallest number of mutually visible pairs of birds, i.e. minimal set of pairs
of mutually visible pairs of birds with
One assumes that a position (point) on
can be occupied simultaneously by several birds, e.g. all possible birds.
![P_1, \ldots, P_{155}](/media/m/4/a/0/4a08ba468aa8a34c3cf6a2d9a3e3a6f5.png)
![C.](/media/m/4/6/7/467f2e8003bd034885e63601825c1836.png)
![P_i, P_j](/media/m/b/6/4/b64a1ae1651bcb3c07a17daa8c1ea39f.png)
![m(\cdot)](/media/m/8/1/d/81d6a70f6c8855927d5b0d88be3c3f54.png)
![m(P_iP_j) \leq 10^{\circ}.](/media/m/f/3/1/f3116cf5554396249bc55b4944e09873.png)
![\{x,y\}](/media/m/3/d/9/3d95866d0ad819208a30af63b68d4e61.png)
![x,y \in \{P_1, \ldots, P_{155}\}.](/media/m/8/d/b/8dbfd87366a8a8fa9573caff7b2646c6.png)
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
Izvor: Međunarodna matematička olimpijada, shortlist 1989