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Puzzling Over Prices

Puzzling Over Prices

The Puzzle Corner activity this week is a thought puzzle that presents an interesting paradox. Solving it will require some divergent thinking on the part of your students. Puzzles like this one appeal to some people, but frustrate others. It is my hope that when students solve this puzzle, or see how it is solved by others, they will be more willing and able to tackle other thought puzzles in the future. It has been my experience that many students who are reluctant puzzle solvers at first become avid fans after being exposed to puzzles on a regular basis. I have also found that, as the teacher, my enthusiasm for puzzles was critical in helping students develop similar enthusiasm.

Please try to solve this puzzle yourself, before giving it to you students. This will give you an idea of what your students will be facing when they try to make sense of the following paradox:

one costs fifty cents, you can buy 12 for one dollar, and 312 for one dollar and fifty cents.

As unlikely as it might seem, this puzzle presents a realistic scenario (at least in states with no sales tax) and will make complete sense, once you figure out what objects are being bought.

Mr. Puh Z. Elle went into Sandy’s Specialty Shop one day to make a purchase. Read their conversation below and then try to answer the question that follows.

SandyShop“Good morning, Mr. Elle.”
“Good morning, Sandy. I’m looking to buy some of these. How much does one cost?
“One? That would be 50 cents.”
“All right, what if I buy 12?”
“Twelve would be one dollar, Mr. Elle.”
“That sounds good. I would like 312.”
“One dollar and 50 cents, please.”
“There you go. Thank you Sandy.”
“You too, Mr. Elle.”

The above story makes perfect sense if you can figure out what Mr. Elle bought. When you do this, it will explain the apparent price discrepancies. What did Mr. Elle buy?

Solution

Click the arrow below to view the solution.

One is 50 cents, 12 is a dollar, and 312 is a dollar and 50 cents. What is being purchased? The numbers one, two, and three were being purchased. Each number costs 50 cents, therefore 312 would be a dollar fifty.

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