In a binary tree with 16 vertices, there must be a path of length 4.

Question

Quizplus · Accepted Answer

In a binary tree with 16 vertices, the minimum height is 4 (since a perfectly balanced binary tree with height 4 has 15 vertices, and adding one more vertex increases the height or maintains it, but still ensures a path of length 4). A path from the root to a leaf node in such a tree (or any deeper node in a less balanced tree) will have a length of at least 4, satisfying the condition.

In a Binary Tree with 16 Vertices, There Must Be