Forming Polygons with Broken Pick-up Chocolate Bars and Spaghetti Noodles
”The broken pick-up sticks problem” is proposed by T. Kyle Petersen and Bridget Eileen Tenner in 2020. We solve the problem by considering the discrete version using random variables, and the limit behaviour of the discrete version gives us a combinatorial solution to the original problem. We also evaluate the probabilities of the triangles formed by the broken/pick-up sticks satisfying some specific geometric conditions with various techniques, including calculus and elementary number theory.