Stage: 4 Challenge Level: 
This one was a tough problem! Some of you started to spot patterns and suggested possible rules, but the patterns didn't continue. In fact, a general rule for this sequence is pretty hard to write down! One very useful way of recording the number of walks of up to eight steps was this:
Can you see how the diagram works? Could you continue it to find the number of ten-step walks?
Dynamical systems. Codes and cryptography. Mathematical reasoning & proof. Fibonacci sequence. Combinatorics. Networks/Graph Theory. epsilons. Patterned numbers. Mathematical induction. Algorithms.
Published September 2000,February 2009.
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