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Discrete Math & Counting Principles

The basics of combinations, permutations, graph theory. These topics are often combined with probability, in which case the problems would then be listed in both categories.
Some of these problems are also in the following subcategories:
 Related Resources

Interactive resources from our Math Tools project:
Math 7: Counting Principles
The closest match in our Ask Dr. Math archives:
Middle School Archive
NCTM Standards:
Data Analysis & Probability Standard for Grades 68
Access to these problems requires a Membership.

Back Yard Trees
 Judy Ann Brown

PreAlgebra, difficulty level 4. How many different quadrilaterals can be formed by joining any four of the nine trees?
... more>>

Basic Breakfast Buffet
 Suzanne Alejandre

PreAlgebra, difficulty level 2. How many days could Linnea, Joel, Karl, and Jakob stay at the hotel
before one of them would
have to repeat one of the breakfasts?
... more>>

Change Woes
 suggested by a Western Oregon University mentor

PreAlgebra, difficulty level 3. What coins did Lacey have before her money was mixed up with her
brother's?
... more>>

Club Competition
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Determine how many teams the Fibonacci Middle School Math Club can enter in their first competition.
... more>>

Coding Conundrums
 Mary DeYoung & class

PreAlgebra, difficulty level 2. Explore encoding and decoding in this cipher puzzle.
... more>>

Colors of the Olympic Rings
 Suzanne Alejandre

PreAlgebra, difficulty level 2. If we categorize all the flags of the world by the combination of the
Olympic ring colors
that appear in them, how many categories would we have?
... more>>

Even Number Puzzle
 Judy Ann Brown

PreAlgebra, difficulty level 3. How many even fourdigit whole numbers exist such that the thousands digit is odd, and all four digits are different?
... more>>

Fall Festival Frolic
 Judy Ann Brown

PreAlgebra, difficulty level 3. How many different types of candy are needed to make at least 50 different treat bags?
... more>>

Flipping Over Pennies
 Judy Ann Brown

PreAlgebra, difficulty level 3. How many equally likely outcomes are there when flipping 10 coins?
... more>>

Kwae
 Suzanne Alejandre

PreAlgebra, difficulty level 3. Determine the number of kwae that can be made.
... more>>

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.
... more>>

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.
... more>>

Money Maker?
 Leigh Nataro, Suzanne Alejandre

PreAlgebra, difficulty level 4. Would you rather earn $10 a week, or take a chance every week on the
money in this paper bag?
... more>>

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.
... more>>

Pegging Possibilities
 Michael Urbut

PreAlgebra, difficulty level 2. Explore the number of possible arrangements of pegs in this logic game.
... more>>

Rampaging Reindeer
 Judy Ann Brown

PreAlgebra, difficulty level 3. How many different ways can Santa's reindeer be arranged?
... more>>

Seating Arrangements
 Judy Ann Brown

PreAlgebra, difficulty level 3. Four new students arrive in Mrs. Brown's homeroom. After a few minutes she turns to them and says, "There are 1680 ways
that you can sit in the empty seats." How many empty seats are there in the room?
... more>>

Student Council Elections
 Judy Ann Brown

PreAlgebra, difficulty level 4. Find the number of ways names can be arranged on the student council ballot, and figure the odds that a brother and sister will both be listed first in their respective races.
... more>>

Totolospi
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Calculate the probability of advancing on a toss when playing the game
Totolospi.
... more>>

TrickorTreat Route
 Judy Ann Brown

PreAlgebra, difficulty level 4. Which of the many possible routes should the Anderson children take on their Halloween trek?
... more>>

Wraparound Universe
 Jeff Weeks

PreAlgebra, difficulty level 4. Explore the game of tictactoe using a cylindrical tictactoe board.
... more>>
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