As a teaser I will present a solution to an old puzzle: n individuals hold n different opinions. Each day a random individual approaches another random individual and the former convinces the latter with his opinion. What is the expected number of days until they all hold the same opinion. A solution can be found here: A Colorful Urn. However, the solution is based on the coalescing duality approach, as will be shown.
Joint work with Itai Arieli, Yakov Babichenko, and Peyton H Young.