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Fibs
The well known Fibonacci sequence is 1 ,1, 2, 3, 5, 8, 13, 21.... How many Fibonacci sequences can you find containing the number 196 as one of the terms?
Gnomon Dimensions
These gnomons appear to have more than a passing connection with the Fibonacci sequence. This problem ask you to investigate some of these connections.
1 Step 2 Step
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
Stage: 3 and 4 Challenge Level: 
Beginners to LOGO programming may want to start by working through the FIRST FORWARD series of introductory articles before tackling this problem.
Below are some examples of recursion. I had been trying to replicate the spirals within the head of a sunflower!
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The program used was:
TO SUNF :S :A
FD :S RT :A
SUNF :S + 1 :A
END
You might like to replicate the spirals above by considering suitable values for the variables :S and :A.
The real challenge is to simulate the head of a sunflower with more spirals that are much more tightly packed and look distinctly more 'Fibonacci' in proportion!
NRICH is part of the family of activities in the Millennium Mathematics Project.