29. Two numbers x and y are selected at random from the interval (0, 1). For i = 0, 1, 2, determine the probability that the integer nearest to x + y is i.

Note: This problem was given by Hilton and Pedersen in the paper “A Role for Untraditional Geometry in the Curriculum,” published in the December 1989 issue of Kolloquium Mathematik-Didaktik der Universit¨at Bayreuth. It is not hard to solve, but it has interesting consequences in arithmetic.