"1. how many ancestors does a node at level n in a binary tree have? provide justification."

In binary tree there are n ancestor at level n.

Proof :

Take P(0): At node level 0, it has no ancestors since this is a roo tnode.

Take P(1): At node level 1, it has one ancestor. The ancestor is the root, its parents which is at level 0.

Take P(K): A node level K it has K ancestors. Its parent is at level K – 1.

Take P(K+1): At node K + 1 level have more than one ancestor than that of node at k level.

Thus there are n ancestor at level n in binary tree.

The first one, i believe, would be correct. all the others have one thing in common, and that's that they have repeating numbers. in the second one, x and y have repeating 6's and 3's, and in the third, x and y have repeating 6's as well. in the last one, there are repeating 3's. the first one has no repeating numbers.

Iam not good at math i wish i could