January 12–January 18, 2010
Problem
In certain rural areas of Russia fortunes were once told in the following way. A girl would hold six long blades of grass in her hand with the ends protruding above and below; another girl would tie together the six upper ends in pairs and then tie together the six lower ends in pairs. If it turned out that the girl had thus tied the six blades of grass into a ring, this foretold that she would get married within a year.
What is the probability that a ring will be formed when the blades of grass are tied at random in this fashion? Solve the same problem for the general case when there are 2n blades of grass.
Solution
List of solvers
Mohammad Hamza, Eric Bensley (undergrad); Lloyd Sakazaki, Congpa You, Wissam Sliman, Joshua Towne (outside).
Eric Bensley wins the prize!