Misleading the witness

14 Bo102010 09 August 2009 08:13PM

Related: Trust in Math

I was reading John Allen Paulos' A Mathematician Plays the Stock Market, in which Paulos relates a version of the well-known "missing dollar" riddle. I had heard it once before, but only vaguely remembered it. If you don't remember it, here it is:

Three people stay in a hotel overnight. The innkeeper tells them that the price for three rooms is $30, so each pays $10.

After the guests go to their rooms, the innkeeper realizes that there is a special discount for groups, and that the guests' total should have only been $25.

The innkeeper gives a bellhop $5 with the instructions to return it to the guests.

The bellhop, not wanting to get change, gives each guest $1 and keeps $2.

Later, the bellhop thinks "Wait - something isn't right. Each guest paid $10. I gave them each back $1, so they each paid $9. $9 times 3 is $27. I kept $2. $27 + $2 is $29. Where did the missing dollar go?"

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