Discussion
In the K3 principle of the central place theory, if the number of settlements are 81, then the hierarchy of settlements from higher to lower order will be as follows :
Answer: B
The hierarchy is 81 (1, 2, 6, 18, 54).
In Christaller's marketing principle (K = 3), each higher-order place serves its own market area plus a third of each of the six surrounding lower-order areas, so the number of places served at each level grows by a factor of three: 1, 3, 9, 27, 81. The number of new centres added at each order is the difference between successive totals:
\[ \begin{aligned} &1,\ 3 - 1 = 2,\ 9 - 3 = 6 \\ &27 - 9 = 18,\ 81 - 27 = 54 \end{aligned} \]
These add up to 81. The other sequences do not grow by the factor of three, and A does not even total 81.
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