MathDB
Math Prize 2023 Problem 7

Source:

October 11, 2023

Problem Statement

An arithmetic expression is created by inserting either a plus sign or a multiplication sign in each of the 11 spaces between consecutive 3\sqrt{3}’s in a row of twelve 3\sqrt{3}’s. The signs are chosen uniformly and independently at random. What is the probability that the resulting expression evaluates to 12312\sqrt{3}?