We will re-enact the story of proving a conjecture by Anders Claesson and Svante Linusson. Along the way, we are naturally led to a particular bijection between matchings and permutations; however, this bijection is somewhat flawed. We will discover a general technique to circumvent these flaws, leading to a new bijection that completes the proof. Time permitting, we will also use this technique to prove a recent conjecture by Miles Jones and Jeffrey Remmel. This talk should be accessible to graduate students of all areas of math.