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Word Problems

Browse Middle School Logic

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Lewis Carroll's Logic Problems [01/15/1997]
Where can I find out more about Lewis Carroll's logic problems?

Lies and Truths... What Day Is It? [04/09/2002]
Jim tells lies on Friday, Saturday, and Sunday. Fred tells lies on Tuesday, Wednesday, and Thursday. Both tell the truth other days. If they both say 'I lied yesterday,' what day is it?

Logic, Groups, and Identities [02/25/1999]
Is it possible for more than one answer to exist when proving things? What is a group? Can you give an example of an identity?

Logic Laws [03/04/2003]
I do not understand the laws of inference, simplification, disjunctive inference, and disjunctive addition.

Match Couples and Parties [03/28/2001]
Read the clues given, and match everything up.

Mathematical Induction [09/07/1998]
What is mathematical induction? Can you give an example of the ideas of math induction?

Mathematics, Logic, and Intuition [05/27/2003]
How is math related to logic and intuition?

Negating Statements [10/27/1998]
What is negation? What is a statement? How do you negate a statement?

Presidential Logic [10/28/2002]
A history test has three questions on Presidents of the United States...

Red and Blue Hats [03/20/2001]
Alan, Ben, and Cal are seated, with their eyes closed. Three hats are placed on their heads from a box that contains three red and two blue hats...

Sets, Subsets, and the Null Set [06/22/2004]
I know that the null set is a subset of any set, but can the null set be an element of a set?

Solving Questions [08/28/2002]
In a poll of 34 students, 16 felt confident solving quantitative comparison questions, 20 felt confident solving multiple choice questions.... How many students felt confident solving only multiple choice questions and no others?

Some Drank All; Did All Drink Some? [02/23/2017]
Three choices lead to too many overlapping preferences. Drawing a Venn diagram, Doctor Peterson fills in some regions with given information, then begins subtracting to deduce intersections and unions.

Three Jars [11/01/2000]
One jar has red marbles, one has black, and one has both, but their labels are wrong. Can you fix the labels by picking one marble from one jar?

To Find the Heavy Marble, Divide and Conquer Asymmetrically [01/14/2011]
A student knows how to deduce the one heavy marble out of eight by weighing successive subsets on a scale balance three times ... but after only two weighings? Doctor Ali suggests the first step.

Train Speed, Wind, and Smoke [7/2/1996]
An electric train is climbing a hill at 45 kph...

Two Mathematicians: Factoring Logic [03/24/2003]
Two mathematicians are each assigned a positive integer. They are told that the product of the two numbers is either 8 or 16. Neither knows the other's number...

Two Mathematicians Problem [05/18/1998]
One mathematician is give the sum of integers X and Y, and another is given their product... what are the numbers?

Unknown Numbers and a Venn Diagram [11/26/2001]
The GCF of two numbers is 20 and the LCM is 840. One of the numbers is 120. Explain how to find the other number and use the Venn diagram method to illustrate.

Valid Arguments [12/17/2002]
What are the real-life applications for valid arguments?

Venn Diagram - Fast Food Restaurants [05/09/2002]
From a list of how many restaurants serve what kinds of food, deduce the total number of restaurants.

Venn Diagram: Goops, Gorps, Gorgs [09/19/2002]
Every Goop is a Gorp. Half of all Gorgs are Gorps. Half of all Gorps are Goops. There are 40 Gorgs and 30 Goops. No Gorg is a Goop. How many Gorps are neither Goops nor Gorgs?

Venn Diagram of Our Number System [12/13/2002]
I don't know how to include complex numbers that consist of a real part and an imaginary part. Can you please diagram this for me?

Venn Diagram to Classify Quadrilaterals [01/02/2003]
I am looking for a Venn diagram that will accurately display the relation among trapezoids, parallelograms, kites, rhombi, rectangles, and squares.

Where is the Prize? [4/17/1996]
"One of these three boxes is filled with precious jewels. The other two contain pebbles from a pond..."

Which Twin is Telling the Truth? [3/2/1996]
At a fork in a road are identical twins. One always lies and one always tells the truth, but you don't know which is which. If you could only ask one question to find out which way to go, what would it be?

Who Gets the Job? [12/11/2001]
Each job candidate can see the other two candidates' black or red dots but not his own. Whoever can figure out the color of his own dot gets the job.

Who Is the Youngest Boy? [04/28/2002]
Al, Ed, and Tom are different ages. One of the following statements is true: Ed is the oldest; Al is not the oldest; Tom is not the youngest. Who is the youngest boy?

Who Made Which Toys? [12/21/1998]
A math logic problem, from a rhyme describing Santa's toymakers.

Who Picked the Most? [09/12/1998]
Arrange the names of the people in the order of the number of peaches that each picked, starting with the person who picked the most.

Why Not Force Dividing by Zero? [10/22/2002]
Has there ever been an attempt to force dividing by zero just as it has been done so successfully by forcing the square root of -1 to be i?

Why the Motionless Runner Parodox Fails [01/01/2005]
I read about the Motionless Runner paradox on your site, and I am now convinced that motion is an illusion. Can you help me understand why the paradox can't be true?

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