Cuisenaire Rod Problems and Fibonacci Numbers
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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?
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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.
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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 ...
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