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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 9-12, 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.

The 2000 Olympics - Leigh Nataro
Discrete Math, difficulty level 4. Use the Borda count method of voting to see which country will host the Olympics. ... more>>

Addition in the Land of Make Believe - Leigh Nataro
Discrete Math, difficulty level 3. For any base b, show that if you subtract the sum of its digits from a number, the result is divisible by b-1. ... more>>

An Apportionment Problem - James Greene
Discrete Math, difficulty level 4. Students apportion the representatives in their class using the Hamilton method of apportionment. ... more>>

Beds of Flowers - Dona Coffey
Discrete Math, difficulty level 2. Dona wants to separate her types of flowers and the colors of her flowers into separate beds. How many beds will she have to dig? ... more>>

Binary Trees - Steve Maurer
Discrete Math, difficulty level 3. Given the definition of binary trees, students discover the relation between interior vertices and leaves and prove that relation. ... more>>

The Bracelet Craze - Leigh Nataro
Discrete Math, difficulty level 3. Find how many ways beads can be arranged around a bracelet. ... more>>

Changing Places - Ethel Breuche
Discrete Math, difficulty level 3. This puzzle requires you to swap chips on an unusual game board. ... more>>

Coding Conundrums - Mary DeYoung & class
Pre-Algebra, difficulty level 2. Explore encoding and decoding in this cipher puzzle. ... more>>

Come Fly With Me - Ethel Breuche
Discrete Math, difficulty level 3. Applicants to the U.S. Air Force are eligible to become airplane pilots only if they satisfy three conditions. Venn diagrams can be used to determine how many applicants actually qualified. ... more>>

The Confession Letter - Ethel Breuche
Discrete Math, difficulty level 1. Students are asked to decode the letter left by the murderer from last week's puzzle. ... more>>

Cooking Dinner - Leigh Nataro
Discrete Math, difficulty level 2. Using graphs and critical paths, find the amount of time it takes to make dinner. ... more>>

The Council of Nations - Leigh Nataro
Discrete Math, difficulty level 4. Use the Webster method of apportionment to divide up the seats for a council of nations. ... more>>

Coverage - Larry Sue
Discrete Math, difficulty level 1. This classic problem asks whether the given shape covers the given grid. ... more>>

The Dating Game - Chuck Biehl
Discrete Math, difficulty level 5. This problem is based on the Stable Marriage Algorithm, which requires students to make the best match possible between a set of girls and a set of boys desiring to date each other. ... more>>

Delivering Toys for the Holidays - Leigh Nataro
Discrete Math, difficulty level 4. Using two different algorithms, find the distance traveled in creating a Hamilton circuit. ... more>>

Deranged Uncle Al - Ethel Breuche
Discrete Math, difficulty level 3. Deranged Uncle Al allows each of his four nephews to select a toy, and buys them the four toys. How many different ways can he give each of the boys a toy so that no boy receives the toy he actually selected? ... more>>

Dona and Dennis Go Traveling - Dona Coffey
Discrete Math, difficulty level 2. Using matrix addition, students determine how many means of transportion they have in getting from city to city. ... more>>

The Doughnut Dilemma - Leigh Nataro
Discrete Math, difficulty level 3. How many ways can you choose three doughnuts from six different types of doughnuts? ... more>>

Fastball or Curveball? - Leigh Nataro
Discrete Math, difficulty level 4. Using game theory, find the percentage of time a batter should guess a fastball will be thrown, and calculate the associated batting average. ... more>>

Field Trip to Fermat's Farm - Leigh Nataro
Discrete Math, difficulty level 4. Going around a circle and skipping every other child, who will be picked to ride Black Beauty first? ... more>>

First Presidential Veto - William Bowdish
Discrete Math, difficulty level 4. This problem involves the Jefferson, Adams, and Webster apportionment methods. ... more>>

The Forever Green Nursery - Leigh Nataro
Discrete Math, difficulty level 3. Does the number of trees in a nursery increase, decrease, or stabilize? ... more>>

The Fourth of July Parade - Ethel Breuche
Discrete Math, difficulty level 3. After the parade, the people on the float I was on shook hands with each other. The Mayor came over and shook hands with only the people he knew. How many people did he know if there were 1625 handshakes altogether? ... more>>

A Game from West Africa - Cara Crosby
Discrete Math, difficulty level 3. This tic-tac-toe like game from Ghana has some good playing strategies and some graph theory applications. ... more>>

A Great Way to Make Money? - Leigh Nataro
Discrete Math, difficulty level 2. Is it better to rely on a weekly pay of $10, or take a chance on the money that is in a paper bag? ... more>>

Gussie the lost Albino Emperor Penquin Pup - Ron Murdoch
Discrete Math, difficulty level 2. Find Gussie, a penguin pup hiding in a zoo building with nineteen rooms, before he suffers from hunger shock. ... more>>

Heads or Tails - Leigh Nataro
Discrete Math, difficulty level 2. Is it possible to have an arrangement of four coins go from HHHH to TTTT based on the rules given for flipping the coins? ... more>>

High School Reunion - Leigh Nataro
Discrete Math, difficulty level 1. Find the minimum number of meeting times needed so that no committee member will miss a meeting. ... more>>

Homework and Candy - Leigh Nataro
Discrete Math, difficulty level 1. Use the Hamilton method to apportion candy among three children. ... more>>

Homework Phone Pals - Leigh Nataro
Discrete Math, difficulty level 1. Using the given clues, figure out which students are homework phone pals. ... more>>

How Many Graphs? - Joseph Rosenstein
Discrete Math, difficulty level 3. How many essentially different graphs are there with six vertices, two of which have degree two, two degree three, and two degree four? ... more>>

The Inside Lines - Larry Sue
Discrete Math, difficulty level 4. This problem makes use of Euler's formula and some geometry to find internal diagonals of regular polyhedra: tetrahedra, octahedra, and icosahedra. ... more>>

Intervals - Stephen Maurer
Discrete Math, difficulty level 3. Students are given clues about intervals on the number line and must determine whether they intersect or not. ... more>>

King Euler's Blueprint - Leigh Nataro
Discrete Math, difficulty level 1. Can you walk a path that will go through every doorway once? ... more>>

The Koch Snowflake - Ethel Breuche
Discrete Math, difficulty level 3. Students are asked to find the length of the side of an equilateral triangle that generated the given Koch Snowflake. ... more>>

Leaping Frogs - Leigh Nataro
Discrete Math, difficulty level 2. Find a formula to determine the number of moves needed to have the frogs switch places on their lily pads. ... more>>

Let's Vote - Leigh Nataro
Discrete Math, difficulty level 3. Create preference schedules that have different winners using the plurality and Borda count methods of voting. ... more>>

The Locker Problem - Ethel Breuche
Discrete Math, difficulty level 2. This classic number theory problem investigates properties of prime numbers, perfect squares, and counting in a problem that involves opening and closing locker doors. ... more>>

Minimal Minnie's Cost - Ethel Breuche, Dona Coffey
Discrete Math, difficulty level 2. Building a rail line that connects a number of different cities: a problem that involves graph theory, minimal cost spanning trees, and algorithms. ... more>>

Mother's Chores - Jim Greene
Discrete Math, difficulty level 1. A Traveling Salesperson Problem. Tom's mother needs to make several stops around the city and then get home. What is her shortest route without going back to one of the stops? ... more>>

Moving the Lincolns - Leigh Nataro
Discrete Math, difficulty level 4. How many moves are needed to turn a triangular array of pennies upside down? ... more>>

Mud Slides and Critical Paths - Ethel Breuche
Discrete Math, difficulty level 4. Can the coastal village rebuild the town after a mudslide before inclement weather returns? Given an order priority digraph, find the earliest completion time and critical path. ... more>>

The Musicians' Dilemma - Daniel Weinstein
Discrete Math, difficulty level 1. The musicians need to cross a bridge but only two may go at a time, using the flashlight. They take different amounts of time to cross but they have only seventeen minutes to get to the concert. How can they do this? ... more>>

New York Tours - Sharon Edelkind
Discrete Math, difficulty level 2. Use vertex coloring to solve conflicting New York tour bus routes. ... more>>

Paper, Scissors, Rock - Leigh Nataro
Discrete Math, difficulty level 2. How many ways can Timmy go broke or win $3 in the game of paper, scissors, rock? ... more>>

Ping Pong Tournament
Discrete Math, difficulty level 3. Organize a Ping Pong (table tennis) singles tournament for your class. ... more>>

Pothole Repair - Leigh Nataro
Discrete Math, difficulty level 2. Plan a route for the road crews to take. ... more>>

Quiz Quandary - Leigh Nataro
Discrete Math, difficulty level 4. Using probabilities and matrices, determine the probability of doing well on a quiz. ... more>>

Rock Star Poisoned - Ethel Breuche
Discrete Math, difficulty level 1. Malonda is found poisoned in her dressing room. Solve this murder mystery using the clues given. ... more>>

Roses, Roses, Roses - Larry Sue
Discrete Math, difficulty level 1. Bob must bring his girlfriend roses to say he's sorry. Explore some of the ramifications of combining modular arithmetic and interpersonal relationships. ... more>>

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