The birthday problem may be related to a coding scheme. Assume we wish to convey a message to an outsider identifying one of the twenty-four people. We could simply communicate a number s from AS = {1, 2, . . . , 24}, having agreed a mapping of people onto numbers; alternatively, we could convey a number from AX = {1, 2, . . . , 365}, identifying the day of the year that is the selected person's birthday (with apologies to leapyearians). [The receiver is assumed to know all the people's birthdays.] What, roughly, is the probability of error of this communication scheme, assuming it is used for a single transmission? What is the capacity of the communication channel, and what is the rate of communication attempted by this scheme?