1. Dinner Bill Splitting. Years ago, my neighbors agreed to celebrate our wedding anniversary with my wife and me. The four of us went to a lovely restaurant, enjoyed a fine dinner, and asked for the bill. When it came, we asked that it be split in half. Realizing the waiter's discomfort, we all set to work on the problem. The bill was for an odd amount, so it could not be split perfectly. However, we realized that, except for the penny problem, we could take half the bill by simply reversing the dollars and the cents. In other words, if we double t dollars and s cents, the result differs by 1 cent from s dollars and t cents. We told the waiter about this. He was astounded: “I never knew you could do it that way.” Later, over another dinner with mathematical friends, the question of uniqueness came up, and pretty soon we realized that this number is the only one with this surprising splitting property. What was the amount of the original bill?

2. The 7-11 Problem. A man goes into a convenience store, picks out four items, and goes to check out. The cashier tells him that her cash register is broken, and she will use her calculator. She proceeds to process the four amounts, and says, “that will be $7.11:” “Wait a minute”, he protests, “you multiplied the prices together.” She promptly repeats the calculation, this time adding the four amounts, and exclaims, “There, you owe $7.11, just as I said.”