The “Birthday Problem,” as posed by Richard von Mises in 1939, is well-known and is often demonstrated in classrooms. The demonstration often involves an informal wager. The teacher may make a claim similar to the following: “I bet that if we check the birthdays of the members of this class, we will find that at least two students have birthdays in the same month and on the same day.” Students love to win any informal wager with a teacher, since one-upmanship can be a powerful motivator. However, how badly do they want to win? What if some students in the class are less than truthful about the date of their birthdays so that they can try to cause the teacher to lose the bet? At the very least, these birthday lies would probably prolong the length of time needed for a birthday match to occur. But how many birthdays do we need to check to achieve the probability of a match that is better than 50 percent? Spencer (1977) dealt with dishonest students in a variation of the birthday problem. Analyzing this situation provides another generalization of the ever-popular classic birthday problem.
Dale Hathaway is especially interested in the mathematics of puzzles and the birthday problem and is currently working on a book about the birthday problem.