Is it possible to draw $6$ circles of equal radius each passing through the centres of exactly three others?
The problem seems to be a direct application of pigeonhole principle but how to use it? May I get a hint?
Here's my take on the Problem : Consider the nodes of the graph as the centres of the circle and the edges as the connection between two circles. Then there will be 9 such edges. Assume that the radius of each circle is $1$ unit. So, how do we ensure that each edge is indeed $\leq 1$ unit?