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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?

Marilyn responds:

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.

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