The Missing Dollar Problem
Three students checked into a hotel and paid the clerk $30 for a room ($10 each). When the hotel manager returned, he noticed that the clerk had incorrectly charged $30 instead of $25 for the room. The manager told the clerk to return $5 to the students. The clerk, knowing that the students would not be able to divide $5 evenly, decided to keep $2 and to give them only $3.
The students were very happy because they paid only $27 for the room ($9 each). However, if they paid $27 and the clerk kept $2, that adds up to $29. What happened to the other Dollar?
Solution
Three students checked into a hotel and paid the clerk $30 for a room ($10 each). When the hotel manager returned, he noticed that the clerk had incorrectly charged $30 instead of $25 for the room. The manager told the clerk to return $5 to the students. The clerk, knowing that the students would not be able to divide $5 evenly, decided to keep $2 and to give them only $3.
The students were very happy because they paid only $27 for the room ($9 each). However, if they paid $27 and the clerk kept $2, that adds up to $29. What happened to the other Dollar?
Solution
Reflection: I enjoy this problem because it is more than just a simple math problem. This problem involves next level thinking because of the wording. Problem solving is present in many different forms and for this problem, it is easy to become confused. One thing I always tell my students is to first write down the facts when dealing with a confusing math problem. It is important to write what you know so you can visually see what you are working with. Many people see this problem as a riddle but since it involves problem solving skills, I do not place it in that category. One of my 5th grade students presented this problem to me while I was student teaching and I immediately found it to be both fun and interesting. I love problems that really make students think and this is definitely one of them.