Two endgame studies!

Both “ingeniously” constructed!

The 1. Puzzle’s 1. move was a true headache to undertake. I love this type of migraine though. (Remembering Aron_08’s Hard-kicking first move recently)

Tricky fellows both of them but I bumped my head fewer times on the road to unpuzzle the second puzzle since it is more up my puzz-alley. Puzzlingly I am more about siege warfare. Not so much open-battlegrounds.

I feel privileged to understand chess rules and coming here knowing a spectacular show of fireworks is just a click round-dah corner. Thank you for that!

I feel sorry for the people that do not know the magical world of chess… What a lose!      

Thanks, @Illbtu! I agree, that first move is incredibly hard to see, which is sort of the point.

The prescription for compositions - other than for games or game combinations - is that no unnecessary/unuseful material should be present in the diagram. Necessary and useful are quite broadly defined to include all material needed in dualfree tries and solution/variations of the assignment. Which is indeed provided for #2 but not for #1. Since the goal is only #4, all material which plays no role in it should be removed.

Many puzzles on chess.com are no compositions precisely because they break the economy rules. Sometimes it is justified because the poster is merely boasting his own game or one of his favorite GM. Here it is only done to erect the illusion of a game position after the composition is already complete. However in a real game no one would care about a mate in 4 over a mate in 5. Not even Fisher in his immortal game

Note that you could change #1 into a "white win" study by removing the #4 assignment, but then you would still have to remove the precise amount of black material to provide a dualfree win. Not that hard to do and the diagram would look much better!

For clarity, #1 and #2 refer to the order of the 2 posted cmpositions, while #4 refers to the "mate in 4 moves"! Sorry if that caused confusion.

FYI: Also note that many endgame studies end in checkmate - but not in a specified number of moves. If a checkmate in 4 is the only way to win, that's great! As soon as a number of moves is specifically demanded, then the composition becomes a "direct mate problem" and is no longer an "endgame study" even when it looks like "endgame material".

Thanks for the tip, @Arisktotle! I changed the checkmate puzzle to this:

Though, the a-pawn only gives black a threat of promotion, so does that make it unnecessary? 

The answer depends on what type of puzzle you want to present. If it is "checkmate in 4 moves" then it is a direct mate problem and you can remove Na6 and Pa3 as well. After all, your solution remains the only one to mate in 4. And it won't lose you any variations of interest.

If on the other hand you want it to be an endgame study then the instruction should be "white wins" and you must make sure that your solution moves are the only way for white to win at all. Then indeed your new setup is just enough to accomplish that - according to StockFish!

So these are very different composition types. Most professional composers make either direct mate problems or endgame studies but not both! They are also judged in different categories and often solved by different solvers. Many problemists like just one of these types. In Holland there are even 2 different organizations for endgame studies and direct mates (+other stuff).

Again the first move! Hard and nice compositions!