Students Find Hidden Fibonacci Sequence in Classic Probability Puzzle

Two students found an unexpected link between the Fibonacci sequence and the "pick-up sticks problem," a probability puzzle. For n random sticks, the probability that no three can form a triangle equals the reciprocal of the product of the first n Fibonacci numbers. This pattern, discovered through simulations by Arthur Sun and Edward Wang, was later proven mathematically. The connection stems from the fact that avoiding triangles requires each stick's length to be at least the sum of the previous two, mirroring the Fibonacci sequence's defining pattern.