Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 3 / 20H / b / Solution

The wedge intersection is simply connected after taking suitable neighbourhoods, so repeated application of the Seifert-van Kampen theorem gives the free product of $n$ copies of $\mathbb{Z}$ withThus, for any basepoint,This is the fundamental group of a wedge of circles and a real projective plane.