I got an old riddle in an email today that’s always been a stumper for a lot of folks. It pops up about once every other year in my inbox and I managed to work out the answer years ago, but it’s still amusing to see that folks are still struggling with it. Different variations on it pop up from time to time, but the basic gist of it is always the same. This latest one reads like this:
Three men go into a motel. The desk clerk said the room was $30, so each man pays $10 and goes to their room. A while later, the desk clerk realizes the room was only $25, so he sends the bellboy to the 3 guys’ room with $5. On the way, the bellboy can’t figure out how to split $5 evenly between 3 men, so he gives each man $1 and keeps the other $2 for himself. This means that the 3 men each paid $9 for the room, which is a total of $27. Add to that the $2 the bellboy kept and the total is $29.
Where is the other dollar?
I know the answer to this one, but I’ll wait before posting it in case folks wanna take a crack at it.
Updated: Here’s the solution:
The answer is: There is no other dollar.
The math isn’t wrong here, the instructions are wrong. Think of the problem this way:
At the end of the day, each man has put in $9 towards the cost of the room: 3 x $9 = $27.
The bellboy has kept $2 from what the men spent for himself: $27 – $2 = $25.
The motel has collected $25.
Or to take it from the other direction:
The motel has $30 and gives $5 of that to the bellboy to return to the men: $30 – $5 = $25.
The bellboy, not knowing how to split $5 equally decides to keep $2 for himself: $5 – $2 = $3.
The men each end up with $1 each. Total it up: 3 x $1 + $2 + $25 = $30.
About the best the bellhop could have done would be to give two men $1.67 and the last $1.66, which would be about as close to evenly dividing $5 he could have come to. The mistake in the instructions is when the riddle asks you to “add the $2 the bellboy kept” to the total the men spent. The bellboy took that money from the total so you would subtract it, not add it. Now, how many of you are slapping your foreheads right about now?