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Browse all Discrete Math Problems of the Week
Participation in the Discrete Math Problems of the
Week allows teachers and students to address the
NCTM
Problem Solving Standard for Grades 912, enabling students to
build new mathematical knowledge through problem solving; solve problems
that arise in mathematics and in other contexts; apply and adapt a
variety of appropriate strategies to solve problems; and monitor and
reflect on the process of mathematical problem solving.
For background information elsewhere on our site, explore the
High School Discrete
Math area of the Ask Dr. Math archives. To find relevant
sites on the Web, browse and search
Discrete Mathematics
in our Internet Mathematics Library.
Access to these problems requires a Membership.

Seating Arrangements
 Leigh Nataro

Discrete Math, difficulty level 3. How many different ways can three people sit at a 10seat counter so that there are empty seats between them?
... more>>

A Series of Numbers
 Ethel Breuche

Discrete Math, difficulty level 3. Find the sum of the first n positive odd integers, find a formula, and prove it.
... more>>

Sokoban
 Stephen Maurer

Discrete Math, difficulty level 3. Solve this game in the fewest number of moves and prove your solution.
... more>>

Sum of a Sequence
 Ethel Breuche

Discrete Math, difficulty level 3. Determine the sum of a sequence of numbers in terms of n: 1, (1+2), (1+2+22),(1+2+2^2+2^3)... (1+2+2^2+2^3...2^(n1) ).
... more>>

The Take Away Game
 Leigh Nataro

Discrete Math, difficulty level 3. Find the strategy to guarantee that you will always win in this game.
... more>>

The Termite and the Cube
 Jared Hammond

Discrete Math, difficulty level 1. Can a termite, traveling only vertically or horizontally through a 3x3x3 Rubiklike cube, go through every cube exactly once and wind up in the very center?
... more>>

Timeline Trivia
 Leigh Nataro

Discrete Math, difficulty level 5. What is the probability of getting all ten historical events in the wrong order?
... more>>

The Tiny Town of Smallsville
 Leigh Nataro

Discrete Math, difficulty level 2. An exercise in recursion: Based on birth and death data, how long will it take the town of Smallsville to double its population?
... more>>

Train Travel
 Dona Coffey

Discrete Math, difficulty level 2. Dona is in charge of setting up a new train service to connect nine towns in a county. What's the minimum cost?
... more>>

Ursala is Undecided
 Melissa Kennedy, Ethel Breuche

Discrete Math, difficulty level 1. Poor Undecided Ursala has many paths to choose to get from point A to point S. Exactly how many paths does she have a choice of taking?
... more>>

Vertices, Edges, and Regions
 Leigh Nataro

Discrete Math, difficulty level 2. Find a relation among vertices, edges, and regions of planar graphs.
... more>>

Voting on Survivor
 Leigh Nataro

Discrete Math, difficulty level 2. Using a modified Borda count method, figure out how many people voted for each preference schedule to produce a tie.
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A Voting Problem
 Leslie Johnson Nielsen

Discrete Math, difficulty level 2. Election theory: investigate the concept of plurality in voting and discuss its fairness.
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Wacky�s Fun and Games Amusement Park
 Natasha Hosein

Discrete Math, difficulty level 4. How can we minimize the number of clowns around the amusement park so that a child will never see two clowns at the same site?
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Welcome Back
 Leigh Nataro

Discrete Math, difficulty level 3. Find the probability of spelling "Welcome Back" when cards with each letter are flipped over.
... more>>

The West Nile Virus Carrying Mosquito Problem
 Lorraine Lurie

Discrete Math, difficulty level 2. Getting the trucks to spray for the virus in all five boroughs involves knowledge of some elementary graph theory and Euler's
theorems regarding traversible graphs.
... more>>

Which is the Dominant Team?
 Jennifer Stetz, Nicole Zayatz

Discrete Math, difficulty level 3. Determine which soccer team dominates the division.
... more>>

Who Broke Mom's Favorite Vase?
 Leigh Nataro

Discrete Math, difficulty level 1. Using logic, determine who is lying and who is telling the truth about who broke Mom's favorite vase.
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Will It Be Pumpkin Pie?
 Leigh Nataro

Discrete Math, difficulty level 4. Based on voting coalitions and power indices, who has more power in deciding what will be served for dessert?
... more>>

Yearbook Deadlines
 Leigh Nataro

Discrete Math, difficulty level 2. Find the critical path to determine the earliest time that the school yearbook can be completed.
... more>>

Your Phone Number, Please
 Ethel Breuche

Discrete Math, difficulty level 1. What is the least number of area codes necessary to guarantee that the thirty million phones needed in a state have distinct tendigit telephone numbers?
... more>>
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