Question 1176930
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The degree of each vertex is either 1 or 2.<br>
A total of 15 vertices with a maximum number of vertices of degree 1 means a minimum number of vertices of degree 2.<br>
The total of 15 vertices will be reached fastest if the vertices in the first few levels of the tree all have degree 2.<br>
Instead of trying to draw binary trees in typed text, I'll make a chart of the numbers of vertices of degree 1 or 2, and the total numbers of vertices, for increasing numbers of levels.<br><pre>
   # of   vertices of  vertices of   total
  levels   degree 2     degree 1    vertices
 --------------------------------------------
     1        0            1           1
     2        1            2           3
     3        3            4           7
     4        7            8          15</pre>
So the maximum number of vertices of degree 1 in a binary tree with 15 vertices is 8.<br>