Funny story. I saw this video yesterday morning, about an hour before my topology exam. One of the questions involved calculating the Euler poincare characteris

Funny story. I saw this video yesterday morning, about an hour before my topology exam. One of the questions involved calculating the Euler poincare characteristic of a 3 fold sum of RP2. Unfortunately, I had forgotten the formula for the case of m-fold sums of RP2 but I knew that it was linear in m and that the Euler poincare characteristic of RP2 was 1. Luckily, I remembered a Klein bottle is homeomorphic to the 2-fold sum of RP2. Having seen this video and knowing the cell complex structure of a mobius band ended up being enough for me to derive the answer.