Puzzling Problems

Is is against the law for a man to marry his widow’s sister? Trick questions like this one almost always pique our interest. We usually delight in these cleverly crafted riddles and brain teasers that catch us off guard. Yet once tricked, most of us are careful not to be tricked again. Anyone who has been snared by the above question is not likely to be fooled by it in the future. (If you have not encountered this question before, try to determine why it is a trick question.) This week’s Puzzle Corner is a collection of trick math questions that will require careful reading and thinking on the part of your students, if they are to be answered correctly. Hopefully, students will take the same delight in these problems (once they discover that they are tricky) that they would in figuring out riddles or trick questions like the one above.

Some educators disparage trick questions like the ones included in this activity. They feel that they have no part in the mathematics classroom, calling them confusing and counterproductive for students. While I can understand why they might feel this way, I believe that the initial confusion can lead to something quite productive for students—the realization that these problems need to be read critically before they are answered. The higher-level thinking that this entails is quite valuable and well worth any initial frustration students may feel when working on problems of this sort.

When you introduce these problems to your class, you’ll have to decide if you want to tell them ahead of time that these are trick questions or let them find this out on their own. For me, the latter option is preferable. Once students discover they have been tricked, they are not as likely to be tricked again and will read future questions more carefully.

Answer the following math problems. Be sure to read them carefully.

1. You have two coins that are worth 30 cents. One of the coins is not a nickel. What are the two coins?

2. Juan had 35 grapes in his lunch pail. He ate all but nine. How many did he have left over?

Girl with Socks3. Nicki has eight identical blue socks and eight identical green socks all mixed up in her sock drawer. If she reaches in without looking, what is the minimum number she must pull out to get a matching pair?

4. How much dirt is in a hole that is one meter deep, two meters wide, and five meters long?

5. A truck can haul 2 tons of rock at a time. How many trips will it take to haul 5 tons?

Solutions

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Puzzling Problems presented a series of trick questions for students to answer. The questions and their solutions are given below:

1. You have two coins that are worth 30 cents. One of the coins is not a nickel. What are the two coins?

You have a nickel and a quarter. The nickel is not a quarter.

2. Juan had 35 grapes in his lunch pail. He ate all but nine. How many did he have left?

He had nine grapes left.

3. Nicki has eight identical blue socks and eight identical green socks all mixed up in her sock drawer. If she reaches in without looking, what is the minimum number she must pull out to get a matching pair?

Three. If she pulls out three socks the possibilities are: three blue, two blue and one green, one blue and two green, or three green. No matter what, she will have a matching pair.

4. How much dirt is in a hole that is one meter deep, two meters wide, and five meters long?

None. Holes don’t have dirt in them.

5. A truck can haul 2 tons of rocks at a time. How many trips will it take to haul 5 tons?

Three trips. You cannot make half a trip.

Dave Youngs

Dave Youngs is director of the Graduate Math/Science Education program at Fresno Pacific University. In this position he works with both pre- and in-service teachers in the areas of math and science education. He is most interested in the elementary and middle school levels.

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