Math Forum - Problem of the Week
Counting Cats and Dogs [Problem #4543]
Lin's math class surveyed all 360 students in their school about their pets.
Here's what they found:
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
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193 of the students have dogs.
160 of the students have cats.
83 of the students have neither a dog nor a cat.
How many students have both a dog and a cat?
Explain how you solved the problem and show how you know your solution works.
Extra: What percent of the students have a cat but not a dog? Explain.
Photo: Kaytee Riek
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Math Forum - Problem of the Week
Rugby Rules! [Problem #5191]
Western's rugby team scored 27 points in their last game. All their points came
from these three ways of scoring:
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
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A try is worth 5 points.
After scoring a try, a team can attempt a conversion, worth 2 points.
A drop goal is worth 3 points.
1. List all the ways they could have scored their 27 points.
2. Explain your strategy for making sure you haven't missed any possibilities.
Remember, you may only attempt a conversion after scoring a try.
Extra: Ben claimed that he scored 4 conversions in that game. Was he telling the truth? How do
you know?
Problem inspired by Ben Comstock, Western Oregon University
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Math Forum - Problem of the Week
Magic Square Jumble [Problem #565]
My friend Magic Square Fifty needs your help. She tripped and fell, and some of her numbers
popped out! If she doesn't put them back in the right place, she will lose her magic power.
To regain some of her magic, all her rows, columns, and diagonals must have the same sum.
To regain all of her magic, each of her quarters (four upper left squares, four upper right squares,
four lower left squares, four lower right squares) and her center (four squares) must have the
same sum.
Can you help her out? She'd be thrilled to have some of her magic back, but she'll offer a bonus if
you can help her get all her magic back.
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Math Forum - Problem of the Week
Sports Weigh In [Problem #5299]
The Math Club at Dawn's school had a Math Carnival. At her booth Dawn set up three scales with baseballs,
tennis balls and soccer balls, as shown in the picture below. Contestants tried to determine the weight of each
kind of ball.
How much does each kind of ball weigh?
Explain how you solved it. Show how you know you are correct.
[Assume that all the soccer balls weigh the same, all the baseballs weigh the same, and all the tennis balls
weigh the same.]
Extra: Find all the other combinations of these kinds of balls that would weigh 22 ounces. Explain how you
found them and how you know you have found them all.
© 1994-2014 Drexel University
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Math Forum - Problem of the Week
Assembly Seating [Problem #17061]
Ben was helping the school custodian set up chairs in the gym for an assembly. They needed to seat 180
students and put the same number of chairs in each row.
After hearing the custodian's plan and doing some quick mental math, Ben suggested a different arrangement
for the same number of seats. He explained that, by putting 5 more chairs in each row, they could have 3
fewer rows, and students in the back row would be able to see better.
How many chairs were in each row of Ben's plan?
Explain how you solved the problem.
Extra: Write a similar problem involving two possible sets of rows and seats per row for 270 students. Show a
solution for your problem.
© 1994-2014 Drexel University
http://mathforum.org/pows/