Let O be the origin of the plane. Imagine that five points, not equal to O, are placed on the plane. Prove that there are two of those points, P and Q, such that the angle anglePOQ is acute. View this problem as an application of the pigeonhole principle. What are the pigeonholes? What are the pigeons? Complete the argument. You generate a random N-bit string, and compute X = summation i to N x_i, where x_i are the 0 and 1 entries of the string. What is the probability that X is odd, if N is odd