Beautiful Binary Trees

The Binary Tree

The Binary Tree

A botanist noticed that a certain species of tree satisfies the following properties:

  • From each end point of the branches (except for the last branch) two new branches arise.
  • There is a leaf at the end of each final branch.
  • Every leaf is an equal number of branches away from the trunk.
  • The Tree has an unique trunk and all branches are of equal length.

He has identified a few trees in a forest: They have 14, 15, 16 and 17 leaves respectively.

Which of these trees could possibly be the one that he's looking for?

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