Creative chess puzzles! What are some of the creative chess problems that can never be solved by computers? Question changed to Creative chess puzzles!

What are some of the creative chess problems that computers can never solve? I'm attaching two examples below so that you can get an idea. My students seem to love these puzzles. I'm researching and learning about it now. Thank you in advance. 




Example 2, 
EDIT
Thanks @ETD for pointing out that it's possible to create programs to solve, at least by brute force solutions to any chess problems. What I mean though is normal chess computers.
EDIT 2: I realize that the question is a bit vague. What I really like to know is creative puzzles, which if given to a beginner player should not be solvable by putting it on his computer and running an analysis.
Here is a fun puzzle:

Construct a legal chess game where


white starts with 1. a3,
white delivers checkmate on move 5, and
the last move is made with the rook that started on a1.



   Hint: Black takes the pawn on a3.