Discussion
A puzzle has 4 possible moves per state and a solution 8 moves deep. How many nodes at the deepest level?
Answer: C
Raising the branching factor to the depth gives:
\[ 4^{8} = 65536 \]
so 65536 nodes at that level, and about 87000 in the whole tree. The bottom level holds three quarters of them, which is the usual pattern. Working an exponential out for concrete numbers, rather than reasoning about it in the abstract, is what makes the growth vivid enough to influence a design decision.
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