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Logic & Set Theory

All Math Forum Problems of the Week could be classified in this category because they require students to explain their reasoning. However, the problems actually categorized here emphasize the
use of logical reasoning or Venn diagrams.
Some of these problems are also in the following subcategories:
 Related Resources

Interactive resources from our Math Tools project:
Math 7: Logic & Set Theory
The closest match in our Ask Dr. Math archives:
Middle School: Logic
NCTM Standards:
Reasoning and Proof Standard for Grades 68
Access to these problems requires a Membership.

Accounting for Age
 Suzanne Alejandre

PreAlgebra, difficulty level 3. Given a number trick, explain why the result is always the original number followed by your age.
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Anjelica's Very Odd Magic Sweater
 Cynthia Lanius, Suzanne Alejandre

PreAlgebra, difficulty level 3. Find the shortcut Angelica's mother might have used to calculate the
number of dimes.
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Balancing Mobiles
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Explore two Laws of Archimedes as you puzzle through a balanced mobile.
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Baseball Attendance Figures
 Judy Ann Brown

PreAlgebra, difficulty level 3. Find the difference between the greatest possible number of people at the stadium and the least possible number of paid admissions to the game.
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Birthday Line Up
 Claire Mead, Stephen Weimar

PreAlgebra, difficulty level 2. How old will Seth be when his mother is five times Seth's age?
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Boxes of Stationery
 Annie Fetter, Suzanne Alejandre

PreAlgebra, difficulty level 3. How many sheets of paper and how many envelopes are in the box of stationery?
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Caliyah's Cart
 Lillian Ray

PreAlgebra, difficulty level 4. How many items did Caliyah decide to buy at the store?
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Car Rental Quandary
 Judy Ann Brown

PreAlgebra, difficulty level 3. Compare the car rental deals using the given information.
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Club Competition
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Determine how many teams the Fibonacci Middle School Math Club can enter in their first competition.
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Coin Count
 Roya Salehi and Judy Ann Brown

PreAlgebra, difficulty level 3. Use the given information to determine the number of nickels and dimes in Lisa's bank.
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Commuting Conundrum
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Help Suzanne and Richard decide which train tickets will give them the most value for their dollar.
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A Cranberry Craving
 Claire Mead, Suzanne Alejandre

PreAlgebra, difficulty level 2. Use the pattern to find out how many cranberries Carissa ate on
Thanksgiving Thursday.
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Duke is Missing
 Judy Ann Brown

PreAlgebra, difficulty level 3. Duke's head is 6 inches long, his tail is as long as his head plus half the length of his body, and his body is as long as the head and tail combined. How long is Duke?
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Eight Squares on a Table
 Suzanne Alejandre

PreAlgebra, difficulty level 3. Find the number written on the first sheet laid on the table and identify which of the eight sheets it was.
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The Graduating Class
 Judy Ann Brown

PreAlgebra, difficulty level 3. Use the information about students with different grades to determine the number of students in Mrs. Smith's class.
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Guess My Number If You Can!
 Judy Ann Brown

PreAlgebra, difficulty level 4. Use division clues to reveal the secret number.
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Happy New Year!
 Judy Ann Brown

PreAlgebra, difficulty level 4. A puzzle for the new year: how is the grid designed?
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Happy Thanksgiving
 Judy Ann Brown

PreAlgebra, difficulty level 3. A logic puzzle to solve the ageold question, "Who will wash the dishes?"
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How Old is Ms. Nelson?
 Judy Ann Brown

PreAlgebra, difficulty level 2. Ms. Nelson claims that she is three times as old as her little sister. However, six years ago she was five times as old as her sister was. How old is Ms. Nelson?
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It's A Secret
 Judy Ann Brown

PreAlgebra, difficulty level 2. In this puzzle, your job is to decode the secret message.
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Label Shuffle
 Judy Ann Brown

PreAlgebra, difficulty level 3. There are three containers. Which one has the red marbles?
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Lemonade Fun
 Maria Fung and her students

PreAlgebra, difficulty level 2. How many cups of each size lemonade did Jose and Nick sell?
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Locker Combinations
 Judy Ann Brown

PreAlgebra, difficulty level 4. In this counting problem you will need to determine the total number of possible locker combinations.
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Lost in Des Moines
 Judy Ann Brown

PreAlgebra, difficulty level 2. Calculate the speed of a car using given information.
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Making Money
 Alice Miller

PreAlgebra, difficulty level 3. How much money would you have by December 31, 1999, if you put 10 cents in the special "math" bank on January 1, 1999?
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Math Club Lollipop Profits
 Judy Ann Brown

Math Fundamentals, difficulty level 3. The Math Club plans to sell lollipops. Help them to calculate their profit.
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Math Club Ski Trip
 Judy Ann Brown

PreAlgebra, difficulty level 2. Mrs. Germain and her friend, Mrs. Granville, need your help to plan the shortest route to visit five local ski areas.
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Measuring Melons
 Suzanne Alejandre, Claire Mead

PreAlgebra, difficulty level 3. Students determine how much each type of fruit weighs.
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Movie Seating
 Maria Fung and her students

PreAlgebra, difficulty level 2. Use the clues to determine where Mom, Dad, Randy, Shelley, Noreen, and Alan sit at the movie theater.
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Mr. Carmel's Party Plan
 Judy Ann Brown

PreAlgebra, difficulty level 2. Help Mr. Carmel's class earn an ice cream party by counting the number of possible sundaes.
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The Name Game
 Judy Ann Brown

PreAlgebra, difficulty level 3. The first student says his/her own name; the second student repeats the first student's name and adds his/her own name... How many names are said if the numbers of students in my math classes on the first day are 27, 28, 32, 31, and 30?
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Operating Diagonally
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Think about the effect of multiplication and addition on the numbers in the hundreds chart.
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The Oracle's Crowns
 Suzanne Alejandre

PreAlgebra, difficulty level 3. Figure out which crown Caleb had on and how he knew for sure.
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The Oracle's Oration
 Annie Fetter

PreAlgebra, difficulty level 3. Explain how payment should be distributed based on the number of rolls two people shared with the group of three.
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Ostrich Llama Count
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Given the combined number of heads and legs of ostriches and llamas, help Raul and Esteban figure out how many ostriches and how many llamas there are.
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Peanut's Back Yard
 Jonathan Bauer

PreAlgebra, difficulty level 3. Peanut, the overexcited dog, makes 40 laps around a stake and travels a total distance of 1 mile. If his bowl of water is 20 feet away from the stake, can he get a drink?
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Pegging Possibilities
 Michael Urbut

PreAlgebra, difficulty level 2. Explore the number of possible arrangements of pegs in this logic game.
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Pouring the Punch
 Neil Bress

PreAlgebra, difficulty level 3. The Refreshments Committee needs to pour exactly four liters of eggnog using only threeliter and fiveliter measures.
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Power Outage
 Jackson Geometry Class

PreAlgebra, difficulty level 3. The power went out. Use the current reading on the clocks to determine when the power went out, and for how long.
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Pumpkin Carving for Charity
 Suzanne Alejandre

PreAlgebra, difficulty level 1. How much money did each of the six friends raise by carving pumpkins
to auction off at a
local charity event?
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Ready for Football?
 Terry Trotter & Suzanne Alejandre

PreAlgebra, difficulty level 2. Find the final score of the game between the Eagles and the Dragons.
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Reversal of Ages
 Terry Trotter

PreAlgebra, difficulty level 2. Using the clues given in the problem, how old are my dad and I today?
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Runsums, Part 1
 Ron Knott

PreAlgebra, difficulty level 3. By spotting the pattern, tell me the smallest number that is a sum of a run of one hundred consecutive numbers.
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Runsums, Part 2
 Ron Knott

PreAlgebra, difficulty level 3. Explore number patterns and report on what you have learned.
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Santa's Little Helpers
 Judy Ann Brown

PreAlgebra, difficulty level 3. Help Santa to solve the puzzle created by the clever elves.
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Seating Dilemma
 Judy Ann Brown

PreAlgebra, difficulty level 2. Count the number of ways to seat people, if some are math teachers who cannot be next to each other.
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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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Snow Day Phone Chain
 Judy Ann Brown

PreAlgebra, difficulty level 4. Use the given information to find out how many phone calls were made.
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A Snowy Driveway
 Claire Mead

PreAlgebra, difficulty level 3. Usually Bertha and Gertrude shovel snow together. How long would it
take Bertha to shovel the same amount alone?
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Square Dancing
 Judy Ann Brown

PreAlgebra, difficulty level 2. The sum of each couple's numbers is a perfect square. Use other information in the problem to find the number of Ashley's partner.
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Study Hall Games
 Judy Ann Brown

PreAlgebra, difficulty level 4. I polled the students to find out which of the three games in my closet they might like to play. Then I created a math problem using the results of the poll.
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Top Notch Nose Contest*
 Judy Ann Brown, Suzanne Alejandre

PreAlgebra, difficulty level 2. Use the given information to determine how many photos of pets were
entered in the contest.
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The Tower of Hanoi Puzzle
 Roya Salehi

PreAlgebra, difficulty level 4. Tower of Hanoi: What is the minimum number of moves it will take to transfer 25 disks from one post to another?
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Train Travel
 Annie Fetter & Ian Underwood

PreAlgebra, difficulty level 2. At what time does the end of the train emerge from the tunnel?
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Tunnel Time
 Annie Fetter, Ian Underwood, Suzanne Alejandre

PreAlgebra, difficulty level 2. At what time does the end of the train emerge from the tunnel?
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Two Heads Are Better Than One
 Lillian Ray

PreAlgebra, difficulty level 3. Given the combined number of heads and legs of ostriches and
pushmipullyus, will
Raquel and Esperanza be able to know for sure how many ostriches and
pushmipullyus
are on the farm?
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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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Wilda's Swamp Water
 Judy Ann Brown

PreAlgebra, difficulty level 3. Measure 8 quibits of swamp water using only 6quibit and 10quibit containers.
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