Problem #PRU-5062

Problem

Eleven people were waiting in line in the rain, each holding an umbrella. They stood closely together, so that the umbrellas of the neighbouring people were touching (see fig.)

The rain stopped and all people closed their umbrellas. They now stood keeping a distance of \(50\) cm between neighbours. By how many times has the queue length decreased? People can be considered points, and umbrellas are circles with a radius of \(50\) cm.