Purchase Solution

Cuisenaire Rod Problems and Fibonacci Numbers

Not what you're looking for?

Ask Custom Question

A) How many different trains of white (1x1) and/or red (1x2) rods are there of a given length N? Find at least 2 ways to justify your solution

b) Can you find an equation to express the number of trains of length N that can be formed using white, red and/or green (1x3) rods?

Purchase this Solution
Solution Summary

Cuisenaire Rod Problems and Fibonacci Numbers are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

Solution Preview

We denote white as 'w', red as 'r', green as 'g'. Let P(N) be the number of different trains.

(a) Let's check some small N's.
When N=1, there is only one train: w. P(1)=1
When N=2, there are 2 trains: ww and r. P(2)=2.
When N=3, there are 3 trains: www, rw, wr. P(3)=3
When N=4, there are 5 trains: wwww,rww,wrw,wwr,rr, P(4)=5.
Suppose there are P(N) trains if the length is N. When the ...

Purchase this Solution
Free BrainMass Quizzes
Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

View More Free Quizzes
Related BrainMass Solutions

  • Proofs of the Fibonacci Sequence

    Step-by-step computations and explanations are shown for both problems. The expert provides proofs of the Fibonacci Sequence.

  • Hogatt's Theorem Proof

    Therefore: The integer can be expressed as a sum of Fibonacci numbers (see assumption: m is smaller than k). So But if m is a sum of Fibonacci numbers and Fn is a Fibonacci number, then k is sum of Fibonacci numbers as well. Q.E.D.

  • Fibonacci numbers: F 2n+1 - Fn Fn+2 = (-1) n

    Fibonacci Numbers :- The Fibonacci numbers are numbers that has the following properties. If Fn represents the nth Fibonacci number, F1 = 1, F2 =1, F3 =2, F4=3, F5 = 5 etc.

  • Fibonacci Number Visual C++ Recursion Iteration Runtime

    In this solution you will learn how to find Fibonacci numbers through a) Recursion and b) Iteration

  • Fibonacci Series

    Each number is the sum of the previous two numbers. Ratios of two successive Fibonacci numbers, show up extensively in nature.

  • Induction Problem with Fibonacci Numbers

    25816 Induction Problem with Fibonacci Numbers The Fibonacci recurrence is F(0) = F(1) = 1, and F(n) = F(n-1) + F(n-2), for n > 1 The values F(0), F(1), F(2), ... form the sequence of Fibonacci numbers, in which each number after the first two is

  • Recurrence Relations: Fibonacci Numbers

    518647 Recurrence Relations: Fibonacci Numbers Show that the Fibonacci numbers satisfy the recurrence relation f_n = 5f_n-4 + 3f_n-5 for n = 5, 6, 7,..., together with the initial f_0 = 0, f_1 = 1, f_2 = 1, f_3 = 2, and f_4 = 3.

  • Theory of Numbers : Fibonacci Numbers

    A Fibonacci proof is provided. The solution is detailed and well presented.

  • Mathematical induction

    91359 Theory of Numbers (VIII): Principle of Mathematical Induction: Fibonacci Number Theory of Numbers (VIII) Principle of Mathematical Induction

View More Related Solutions