Three students rent a room in a hotel and pay the desk clerk $60 for the room. The night clerk comes on duty and notes that the discounted rate for students should have been $55. The new clerk gives the bellhop $5 to return to the students, but the bellhop needs some extra cash, so he returns only $1 to each of the three students and keeps the remaining $2.

Each student now paid $20-$1 = $19, and 3 x $19 = $57 paid in total. The bellhop kept $2, for a total of $59. What happened to the extra $1?

Produce a diagram that illustrates the flow of money, with a box for each of the five individuals (three students, clerk, and bellhop). Put in the final money paid or received in the box for each individual and show the money transfers between boxes with arrows;

Perform a money balance, showing the net results among the five individuals (three students, clerk, and bellhop);

Can you determine why the logic in the problem is faulty?