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Logical Reasoning

Problems that require students to think in a logical and organized fashion in order to reach a conclusion.
 Related Resources

The closest match in our Ask Dr. Math archives:
Elementary Puzzles
NCTM Standards:
Reasoning and Proof Standard for Grades 35
Access to these problems requires a Membership.

A Pound of Tea
 Claire Mead

Math Fundamentals, difficulty level 3. Find out how long a pound of tea would last Hazel if she were alone.
... more>>

Baseball Cards
 Claire Mead

Math Fundamentals, difficulty level 2. How many cards does each of the three boys have in his baseball card collection?
... more>>

Bobsled Sums
 Bob and Claire Mead

Math Fundamentals, difficulty level 3. Find which men rode with driver number 1 on his fourman bobsled.
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Building Barns *
 Claire Mead

Math Fundamentals, difficulty level 3. How long will it take Amy's crew to build a barn?
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Campfire Camaraderie
 Jessica Philips from Western Oregon University

Math Fundamentals, difficulty level 1. How did the animals place themselves around the campfire?
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Change You Can't Count On
 Claire Mead

Math Fundamentals, difficulty level 2. What is the greatest amount of money I can have in my pocket?
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Chelsea's Number Puzzle
 Claire Mead

Math Fundamentals, difficulty level 2. Help Chelsea solve this addition number puzzle using the numbers 1 through 9.
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Clock Work
 Claire Mead

Math Fundamentals, difficulty level 2. How did Maria and Sammy arrange their pencils on the clock face?
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Counting Cats and Dogs
 Claire Mead

Math Fundamentals, difficulty level 2. How many students in Lin's school have both a dog and a cat?
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Crossing the River with Ogres
 Claire Mead

Math Fundamentals, difficulty level 2. Find out how many times the boat must cross the river to get all the
gnomes and ogres to
the other side.
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Dashing Through the Snow
 Claire Mead

Math Fundamentals, difficulty level 3. Use clues to determine the finishing order of the ski racers at Winter Carnival.
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Dragons and Tigers and Hares, Oh My!
 Claire Mead

Math Fundamentals, difficulty level 3. Use clues about the Chinese calendar to determine when Lin's greatgrandfather was born
and how old he is.
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Elevator Weighin
 Kristina Lasher

Math Fundamentals, difficulty level 2. Would Melissa's family and neigbors exceed the maximum weight allowance of their apartment building elevator? If not, how many more would fit?
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Emmy's Action Figures
 Claire Mead

Math Fundamentals, difficulty level 2. In how many different ways can Emmy arrange her Famous Mathematician
action figures?
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The Farmer in the Dilemma
 Claire Mead

Math Fundamentals, difficulty level 3. Help Farmer Mead spend exactly $100 buying exactly 100 sheep, cows and
horses.
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Four Playful Mathematicians
 inspired by Maria Fung's class at Western Oregon

Math Fundamentals, difficulty level 2. Follow the clues to help the four playful mathematicians return the lost watch.
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Funny Money
 Lisa Lavelle (adapted)

Math Fundamentals, difficulty level 2. Determine the amount of money Divya has in her bank.
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Grampa Joe's Great Grandpets
 Kristina Lasher

Math Fundamentals, difficulty level 1. Grampa Joe is taking gifts to his grandchildren for their new pets. Can you help him figure out which great grandpet belongs to each grandchild?
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Holiday Ornaments
 Claire Mead

Math Fundamentals, difficulty level 3. How many holiday ornaments did each girl's mother make?
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Hot Dog Day!
 Jeffrey Mo

Math Fundamentals, difficulty level 3. Determine how many large hot dogs have been ordered for this special day.
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How Old is Dad?
 Claire Mead

Math Fundamentals, difficulty level 2. Use the clues to find out how old Dad is.
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In Their Prime
 Claire Mead

Math Fundamentals, difficulty level 2. Use the clues about multiples and primes to figure out how old
Jonathan and Hazel are.
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Let the Chips Fall . . .
 Claire Mead

Math Fundamentals, difficulty level 3. Use clues about sums to determine which digits are on the reverse sides of three
given chips.
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Magic Square Jumble
 Lisa Lavelle

Math Fundamentals, difficulty level 3. Help straighten out this magic square.
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Marble Mayhem
 Claire Mead

Math Fundamentals, difficulty level 2. Fred and his friends divide the marbles in several different ways, but
there is always one left
over.
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March Madness!
 Teaching the Young Learner Class

Math Fundamentals, difficulty level 3. Given four clues, figure out which pair of friends won a basketball game.
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Math Club Field Trip
 Claire Mead

Math Fundamentals, difficulty level 3. How many people returned from the Math Club field trip in Miss Noether's van?
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More Balloons
 Lisa Lavelle

Math Fundamentals, difficulty level 5. Here's a more difficult problem based on our balloon color preferences.
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Multiplication Mystery
 Ya. I. Perelman (translated from Russian by Valentina Sokolskaya)

Math Fundamentals, difficulty level 3. Decipher this cryptic multiplication problem to uncover the final product.
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Nuts in a Bowl
 Claire Mead

Math Fundamentals, difficulty level 3. Determine how many nuts are in five bowls using the given clues.
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Price Tag Repair
 Teaching the Young Learner Group

Math Fundamentals, difficulty level 2. Can you use the clues to help Cathy repair the price tags for the family yard sale?
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Salad Daze *
 Claire Mead

Math Fundamentals, difficulty level 3. How many students in Ashley's class put no tomato, carrot or cucumber
on their salads?
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School, Who Has Time?
 Lisa Lavelle (old remembered puzzle)

Math Fundamentals, difficulty level 3. Given all the time we spend doing other things, how do we have time for school?
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Sharing Smelt
 Claire Mead

Math Fundamentals, difficulty level 3. Find out how many smelt Larry caught Saturday morning.
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She Counts Seashells *
 Claire Mead

Math Fundamentals, difficulty level 2. How many shells does Marcia have in her collection?
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Siblings
 Claire Mead

Math Fundamentals, difficulty level 2. Use clues to find out how many boys and girls are in Alex's family.
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A Simple Reversal
 Judy Ann Brown

Math Fundamentals, difficulty level 1. The product of 3 and 24 is 72. The sum of 3 and 24 is 27, which is the reverse of 72. Can you find other pairs of numbers such that their product is the reverse of their sum?
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Sports Weigh In
 Claire Mead

Math Fundamentals, difficulty level 3. Use three scale readings to find the weight of the soccer ball, the
tennis ball, and the
baseball.
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Subway Tokens
 Annie Fetter and Claire Mead

Math Fundamentals, difficulty level 2. How did Samantha know the subway token machine didn't behave as advertised?
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Summer Shoe Leftovers
 Teaching the Young Learner Group

Math Fundamentals, difficulty level 4. Determine which of the leftover shoes might satisfy three shoppers' needs.
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Sundaes
 Claire Mead

Math Fundamentals, difficulty level 3. How many children had no topping on their ice cream?
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Team Tag
 Corinne MacPherson (adapted from Faces of Mathematics by A. Wayne Roberts)

Elementary, difficulty level 3. In the game of Team Tag, each kid (excluding Allison) earned a different number of points. How many points did Allison's teammate Jenny earn?
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What Day Is It Today?
 Roya Salehi

Math Fundamentals, difficulty level 2. Sophie tells the truth only on Monday, Tuesday, Wednesday, and Thursday. Her sister tells the truth only on Monday, Friday, Saturday, and Sunday. If they both confess to their mom that "Yesterday I lied," what day is it today?
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Zelma's ZIP Code
 Claire Mead

Math Fundamentals, difficulty level 3. Find Zelma's Zip Code by ordering pairs of digits that are products of onedigit numbers.
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