Wednesday, February 28, 2007

The $30 motel room puzzle

Three travelers came to a motel and decide to share one room. The clerk registered them for $30. Each of the travelers pitched in $10. After a bit, the clerk realized that the special rate for that day was $25, so he gave the bellhop $5 and told him to take it to the travelers. On his way to the room, the bellhop reasoned that he couldn't split $5 three ways, so he'd just return $3 to the travelers and keep the other $2.

Therefore, each of the travelers wound up paying $9 for his room. Since 9 X 3 is 27, and the bellhop kept $2, what happened to the other dollar (27 + 2 = 29)?

You may or may not have heard this puzzle before. It is an interesting one, in the way the question is posed.

A simple cash flow and balance statement will throw a lot of light on the transactions.

Travelers ______Clerk ______Bellhop
-10x3 = -30 _____+30 ________0
-30 ___________+25 +5 ______0
-30 ___________+25 ________+5
-30 ___________+25 ________+3+2
-30+3=-27______+25 ________+3+2-3=+2

Final transaction:
-9x3=-27 _______+25 ________+2

Notice that each line balances itself. The final result is that the travelers paid $27, and the clerk kept $25 and the bellhop $2. So, everything balances.

What throws people off is the reference to the original $30 that everybody started off with.

Putting the transaction down on paper as a cash flow statement makes things a lot more clear.

Anyway, this is the way I looked at it. Let me know if you have any other ways of analyzing it.