See also the
Dr. Math FAQ:
3D and higher
Browse Middle School Logic
Stars indicate particularly interesting answers or
good places to begin browsing.
- 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
- 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
- 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
- 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?
- 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
- 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
- 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,
- 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
- 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
- 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?