Puzzle #1 – Solution

The key observation to the solution of this puzzle is to note that the outputs of components can be connected together given than only one drives a non high-Z value. If you realized that 90% of the way to solving this puzzle is behind you.

The second step is to realize a “NOT” gate using both the “X” and “Y” components. When you know how to do that an “OR” and an “AND” gate realization are quite simple.
The figure below sums up the construction of “NOT”, “OR” and “AND gates from various instances of “X” and “Y”.

The next step is quite straightforward. We combine the gates we constructed and make an “XOR” gate as follows:

This is by no means the most efficient solution in terms of minimum “X” and “Y” components.