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**Unformatted text preview: **these are the Fibonacci
numbers.
12 The Mad Scientist’ Problem
s
We want to make a chain out of pieces of Lead
and Plutonium. The chain is supposed to be of
length n. However, there is a problem: if we
put two pieces of Plutonium next to each other,
the whole chain will explode. How many safe
chains are there. (Note: These are linear
chains.) C(n) = Number of Safe Chains of length n.
L(n) = The number of safe chains of length n
that END with a piece of lead.
P(n) = The number of safe chains of length n
that END with a piece of Plutonium. 13 Example: Length = 3
s LLL
s LLP
s LPL
u LPP s PLL
s PLP
u PPL
u PPP 14 The total number of chains must be the sum of
those that end with Lead and t...

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