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High School Archive

Browse High School Discrete Math
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Four-color map theorem.
    How many handshakes?
    Squares in a checkerboard.
    Tournament scheduling.
    Venn diagrams.

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Dates that Read the Same Backwards and Forwards [02/02/2010]

A student sees a palindrome in the date 01 02 2010, and wonders how to generate all such palindromic dates. Building on another math doctor's work with date arithmetic, Doctor Carter shares a program written in C, then goes on to explain the purpose of each line of code.

Derfs and Enajs: Algebra and Venn Diagrams [03/09/2003]

All Derfs are Enajs. One-third of all Enajs are Derfs. Half of all Sivads are Enajs. One Sivad is a Derf. Eight Sivads are Enajs. The number of Enajs is 90. How many Enajs are neither Derfs nor Sivads?

Diagram for Math Numbers [10/05/1997]

My daughter is doing a tree diagram using terms related to math "numbers." Could you please explain in lay terms what surds are?

Dinner Triplets [10/23/2000]

A woman has 15 friends. For 35 days she wants to have dinner with 3 friends a day, arranging it so that each pair of friends will come only once. Is this possible?

Discrete versus Continuous [08/24/1998]

What is discrete math? How do you use it?

Divisibility and Remainders [8/23/1996]

Show that every odd square leaves a remainder 1 when divided by 8... Prove that n^5-n is divisible by 30... Suppose m is a positive integer divisible by 11...

Duotrigesimal (Base 32) Numbers [06/11/1999]

A unique and interesting use for base 32 or "duotrigesimal" numbers.

Electoral math units [6/16/1996]

Any suggestions for units on electoral math, for use with students in grades 7-9, with plenty of entry points for both beginning and advanced students?

Employee Scheduling [09/22/1998]

Can you help me make a schedule to staff an ice cream parlor?

Equivalence Classes [02/19/1999]

Is there an equivalence class containing exactly 271 elements?

Equivalence Relations [10/02/1998]

Let X = {people in the world} and R be a relation on the set X... find the equivalence classes.

Eulerian and Hamiltonian Tours [1/27/1996]

I am looking for a few simple applications of Eulerian and Hamiltonian tours - real-world applications for 8th grade students.

Even - Odd Handshake Problem [05/11/2000]

How can I prove that the number of persons who have shaken an odd number of hands is even?

Examples of the Fundamental Counting Principle [02/17/2001]

There are three ways to go from Town A to Town B, and four ways to go from Town B to Town C. How many different ways are there to go from Town A to Town C, passing through Town B?

An Explanation of Some Latin Math Terms [12/11/1995]

We are a small discrete math class of eight students studying logical arguments. Two arguments we have examined are "modus tollens" and "modus ponens." We understand the arguments but would like to know what the terms mean in English.

Exponential Growth on a Family Tree [12/26/2002]

What is the probability of my being related to a famous person of the past?

Factorials Can't Be Squares [02/11/2000]

Can you prove that the factorial of a number (greater than 1) can never be a perfect square?

Factoring [02/09/1999]

Find the smallest number (integer) that has 30 factors.

Factors and Multiples - Hamiltonian Path [11/02/1998]

We have to make a sequence of numbers, all different, each of which is a factor or a multiple of the one preceding it.

Fermat's Last Theorem and Chess [3/25/1996]

I'd like to know if Fermat's problem is solved, and when chess is likely to be solved.

Fewest Number of Stops [09/12/2001]

At some stops, the SLU Express bus picks up 5 people. At other stops, it picks up 2 and lets off 5...

Finding a Non-Recursive Formula [06/10/1999]

How can I find a non-recursive formula for the recurrence relation s_n = - [s_(n-1)] - n^2 with the initial condition s_0 = 3?

Finding Formulas for Number Sequences [11/22/1997]

My question is about trying to find a formula between numbers.

Finding Howlers [10/25/1999]

Howlers are fractions like 16/64; when you cross out the 6 on the top and the bottom, you are left with 1/4, which is the simplified fraction. How can I find all 2-digit, 3-digit and 4-digit howlers?

Finding Numbers with a Certain Number of Factors [3/12/1996]

Given that twelve is the least positive integer with six different positive factors (1,2,3,4,6,12), what is the least positive integer with exactly twenty-four positive factors?

Finding Pathways [04/08/1999]

How many ways are there to get from top left to bottom right on a square when there are three lines going across each way?

Finding the nth Term [03/28/2002]

My formula works with the exception of the first term.

Five-Set Venn Diagram? [11/25/2001]

What does a five-set Venn diagram look like?

Floor and Ceiling [05/28/2000]

What do 'floor' and 'ceiling' mean in mathematics?

Formula for Connection between Rows of Pascal's Triangle [11/15/2003]

Find a formula connecting any (k+1) coefficients in the nth row of the Pascal Triangle with a single coefficient in the (n+k)th row.

Formula for Factors of a Number [11/3/1996]

How many triangles can you draw on a square grid of dots of size x*x?

Four-Color Map Problem [12/8/1994]

Other than trial and error is there any scientific or mathematical way to solve the Four Color Problem? How about even explaining it in layman's terms?

Four Colors, Eighths of a Circle [10/15/2001]

Divide a circle in eighths. Use 4 colors to color the segments. Colors may be repeated as long as you use all 4 colors at least once. What are the total combinations possible?

Four-Color Theorem [4/13/1996]

If you wish to color in each "country" or "space" on a map in such a way that no two contiguous countries or spaces have the same color, what is the minimum number of colors you can use?

Four-Color Theorem - sci-math faq [8/21/1996]

Do we need more than four colors to color a two-dimensional map?

The Game of NIM [1/31/1995]

The game of NIM is played with a bunch of beans....

Generating Eight-Character Passwords [03/08/2002]

Given some restrictions, calculate the number of possible 8-character passwords.

Generating Possible Lottery Outcomes [3/29/1996]

What math rule would I need to follow if I wanted to generate all possible combinations in a 50 number draw 6 lottery?

Graphs - Proving the Infinite Ramsey Theory [11/10/1997]

In a graph with infinite "points," if we colour the lines with two colors we'll have either a red or a blue infinite chain of lines, an infinite number of points, all of them joined to each other with the same colour...

Graphs with Three Vertices [03/31/1999]

What are graphs with three vertices? Could you give me some examples?

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