Problem

Source: Kyiv mathematical festival 2016

Tags: Kyiv mathematical festival, combinatorial geometry, combinatorics



1) Is it possible to place five circles on the plane in such way that each circle has exactly 5 common points with other circles? 2) Is it possible to place five circles on the plane in such way that each circle has exactly 6 common points with other circles? 3) Is it possible to place five circles on the plane in such way that each circle has exactly 7 common points with other circles?