Several coins with collinear centers
Source: XVII Sharygin Correspondence Round, P12
March 2, 2021
geometry
Problem Statement
Suppose we have ten coins with radii cm. We can put two of them on the table in such a way that they touch each other, after that we can add the coins in such a way that each new coin touches at least two of previous ones. The new coin cannot cover a previous one. Can we put several coins in such a way that the centers of some three coins are collinear?