Three men pay $30 as a group to rent a room. The clerk discovers he has overcharged the group $5 and he gives the bellhop the money to return to the three men. The bellhop decides that $5 is too hard to divide by three and then he gives each man a dollar each and keeps the remaining $2 for himself. The three men have paid $9 each, the bellhop has kept $2, making $29. Where did the extra dollar go?
ANSWER:
Words and the way words are arranged play a significant role in the way we approach problems. This problem is structured so that we focus on how to divide the $5 by three and end up losing a dollar. We’re looking at the wrong things. To find the missing dollar, subtract the $3 the bellhop returns to the men from the original $30. This leaves $27. Then subtract the bellhop’s stolen two dollars (27 -2 = 25). Now all the money ($30) is accounted for. $25 for the room, $3 returned to the men, $2 stolen by the bellhop.
EXPLANATION:
Thought is fluid. When you frame a problem in words, you crystallize your thoughts. Words give articulation and precision to vague images and hazy intuitions. But a crystal is no longer fluid and committing yourself to the first words that come to mind may disrupt your thought process.
Consider the following problem:
Water lilies double in area every twenty-four hours. On the first day of summer, there is one water lily on the lake. Sixty days later, the lake is completely covered with water lilies. On which day is the lake half covered?
The words “double,” “twenty-four,” “one,” “on which day,” and “sixty” coax most people to divide the sixty days by two and propose the thirtieth day as the solution, but since the lilies increase in area geometrically, this is incorrect. The lilies cover half the pond on the next-to-last day. The word structure of the problem influences us to come up with the incorrect answer.
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