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Ask Marilyn: Can You Solve This Classic Hotel Room Riddle?
Mike Kosko in Bethlehem, Pennsylvania, writes:
Marilyn: Can you please provide the math equation that will solve this riddle? Three businessmen go to a hotel. The desk clerk tells them they can have a special rate: $30 for sharing a room for one night. They each take out $10, hand it to the clerk, and go to the room. The clerk then realizes he made a mistake. The special rate was $25 for the room. So he gives the bellman $5 in singles and tells him to take it up to the guests. The bellman needs money, so he keeps $2 for himself and gives each man $1, instead. In effect, each guest has paid $9 (his original $10 minus the $1 he got back). So they each paid $9, a total of $27 for the three, plus $2 the bellman put in his pocket. That equals $29. What happened to the other dollar?
No math equation applies because the logic is incorrect. No dollar is missing. You added the amount the three men no longer have ($27) to the amount the bellman does have ($2), which doesn't make sense. That total ($29) happens to be close to the original price of the room ($30), which may mislead a reader into thinking the two numbers are related. But they are not.
You can easily account for the $30 by adding where the money is, not where it is not! The desk clerk has $25, the three men have $3 ($1 each), and the bellman has $2. 25 + $3 + $2 = $30.