On the campus of

# Cab Conundrum

This week’s puzzle is a modification of a brain teaser that has been around for many years—the hotel problem. In the original version of the mathematical paradox, three men pay ten dollars each for a thirty dollar hotel room. Later, they receive a five dollar refund. Because they cannot easily split the five dollars, they each keep one dollar and give the bellboy a two dollar tip. Thus, each man’s share of the room is nine dollars. Nine dollars multiplied by three is twenty-seven dollars. When the two dollar tip is added, the total is twenty-nine dollars. The conundrum comes in determining what happened to the missing dollar. In the modification presented here, the paradox is the same, but the setting is slightly different. The challenge remains for students to find the missing dollar.

Each student should be encouraged to persevere in discovering a solution and not to share the answer with their classmates once it is discovered.

Solution Hint: Think about what is being added to reach the total of twenty-nine dollars.

Three men agree to share a cab from the airport into town. When they arrive, the meter reads \$25. Each man gives the driver a \$10 bill. She hands them five \$1 bills as change. Each man takes one of the \$1 bills. They give the driver the remaining two \$1 bills as a tip.

Each man has now spent nine dollars, and the driver has two dollars, bringing the total to \$29 (3 x 9 = 27, 27 + 2 = 29). What happened to the other dollar?