Trees?

May 2010
12
0
Okay, so here's my question:

Every full 4-ary tree of height 2 has at least ________ vertices and at most ________ vertices.


I know the formula to find the max number of leaves is m^h leaves in an m-ary tree of height h.

However, I don't know how to find max/min number of vertices. Any suggestions?


EDIT: Okay, so I used the max number of leaves formula (m^h) to get the max possible number of leaves for my 4-ary tree. The answer is 16. So, I got to thinking, what if I use the formula n = (ml - 1)/(m-1) (n being vertices, m being the m-ary tree, and l being the leaves). I plugged everything in and got 21. Is this the answer of the max vertices? If so, how do I get the min?
 
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