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Discrete Math: Patterns and Recursion

Working with a simpler example and then observing patterns is key to solving many of the following problems. Some of these problems, like the Forever Green Nursery problem, are based on a recursive pattern. Recursive patterns occur when the outcome of a step is dependent on the outcome of a previous step.

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.

Count Your Seinneps - Leigh Nataro
Trig/Calc, difficulty level 2. Find a system of coins that uses the fewest number of coins possible without repeating coins. ... 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>>

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>>

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 Me Guess Your Number - Leigh Nataro
Trig/Calc, difficulty level 3. Discover the patterns behind a number puzzle. ... 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>>

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>>

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

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