Question

Suppose you owe 10 dollars to a friend. Each week you pay your friend at least 1 dollar back. Sometimes however you might pay your friend back 2 dollars in a week and other times you might pay your friend 5 dollars in a week. How many different payment sequences are possible

Answer 1

Answer: if you give your friend one dollar the first week you’d only owe 9 dollars left. Then the second week you play the 2 dollars, you now only owe 7 dollars. The third week comes and you give them 5, you only owe 2 dollars. Then you’d only be able to give them 2 dollars the next week, or one dollar then another one the following week. There are 4,5 different payment sequences possible.

Explanation: