09 Apr The Riddle of the Missing Dollar (JIM AL-KHALILI)
Three travelers check into a hotel for the night. The young man at the reception desk charges them $30 for a room with three beds in it. They agree to split the price of the room equally, each of them paying $10. They take the key and head up to the room to settle in. After a few minutes the receptionist realizes he has made a mistake. The hotel has a special offer on all week and he should only have charged them $25for the room. So as not to get into trouble with his manager, he quickly takes five dollar bills from the till and rushes up to rectify his error. On the way to the room he realizes that he cannot split the five dollars equally between the three men, so he decides to give each of them one dollar and keep two for himself. That way, he argues, everyone is happy. Here, then, is the problem we are left with each of the three friends will have contributed $9 toward the room. That makes $27that the hotel has made, and the receptionist has a further $2, which makes $29. What has happened to the last dollar out of the original $30?
You may be able to see the solution to this straightaway; I certainly didn’t when I first heard it. So I will let you think about it a little before you read on.
Have you worked it out? You see, this puzzle only sounds paradoxical because of the misleading way it is stated. The error in the reasoning is that I added the $27 dollars to the $2 taken by the receptionist—and there is no reason to do that, because there is no longer a total of $30 that needs to be accounted for.
The receptionist’s $2 should be subtracted from the $27 paid by the friends, leaving $25, which is the amount in the till.