I'll give it a try.
First puzzle:
It's black to move, so to take back black's last move first we have to take back white's last move.
edit, oh, you want the answer in text only? Ok, I'll delete the diagram. I think this makes it a lot harder to understand though.
White takes back Bxf7
Black takes back Nxf7 and instead plays Nh3
White plays Qg7 mate
Same sort of trick for the 2nd puzzle. For example white's last move was queen from b3 to g8+ (black king on f8). So instead white plays Qb8 mate.
Thank you for the reply!
Retro-instructions sometimes look unclear. The intention for both diagrams is that white is on move, so black starts by retracting his last move. Which gives us the following format for the required solutions:
A-problem: 1 retraction move, 2 forward moves
B-problem: 2 retraction moves, 1 forward move.
In spite of the confusion, your moves in the B-problem are indeed precisely 2 retraction moves and 1 forward move as intended. So that part is OK. There is however a chess rule which you overlooked and which makes your solution illegal. Try to figure out what it is.
I will modify the diagrams and text somewhat to provide more clarity! (Done!)
Oh, ok.
For the 2nd one, what's the rule? I don't think the position is impossible, for example black's last move could have been with the bishop.
Sorry, I can't tell you 
It's a major part of the challenge. The rule I am referring to has been with us for about 25 years and you can find it in the basic rules of play of the FIDE laws.
King on f8, queen on b3, Qb8 mate.
I'm afraid I'm not going to be able to figure out what's illegal about that (but I might still misunderstand the puzzles)
Ok, first one I'm guessing black's last move was KxB on h8.
Instead of that black plays Kf8 and now white plays Bg7 mate?
Ok, first one I'm guessing black's last move was KxB on h8.
Instead of that black plays Kf8 and now white plays Bg7 mate?
Yabba-dabba-doo! Told you that one was (relatively) easy. You can pick whatever retraction moves you like as long as they are legal.
2nd puzzle:
There was a white queen on e6 and the black king was on f8. White could have played Qf7# but instead played Qg8+?? Kxg8.
King on f8, queen on b3, Qb8 mate.
I'm afraid I'm not going to be able to figure out what's illegal about that (but I might still misunderstand the puzzles)
There is nothing illegal about that. If you can't find the applicable FIDE law, wait for me to post the full solutions.
2nd puzzle:
Thanks! Your solution is similar to that of Chebyshevv and it has the same flaw. Please read my replies to him. Can't reveal more I'm afraid.
Maybe easy for you, but it took me a while
That's why I make these puzzles. Can't stand the frustation of missing the solution 
Your chess viewer is wrong. Never trust chess engines and chess viewers :-)
Hint:
Bruce Willis
Hint:r
Great! Bruce allmighty has arrived. Is puzzle "B" new? Or is it already in your database?
Hint:r
Great! Bruce allmighty has arrived. Is puzzle "B" new? Or is it already in your database?
It's new to me, but I didn't understand what a retractor was in those days. It's the sequel that allows us to decide which of the two possible last moves we want.
It's new to me, but I didn't understand what a retractor was in those days. It's the sequel that allows us to decide which of the two possible last moves we want.
I usually go for the "fait accompli" narrative which is the foundation of the help-retractor: "we tell you (=give you the extra information) that white could have checkmated on a previous occasion".
But good to know that it is uncharted territory. Keeps me occupied for the next few Christmases!
Beware when Arisktotle announces simple puzzles. You might expect them to be as treacherous as the simple Simon puzzles in "Die hard with Bruce Willis
" - a promise which never appears to come to fruition.
Then again, you can trust these puzzles to be in accordance with the chess rules and you can rely on Arisktotle to release the post-mortem analysis you are willing to die for - not before Christmas though!
The seasonal flavour of december puzzles is retrograde and I'll stick with that convention. The first one of the 2 simple puzzles is the easiest; for the second one you require a good knowledge of all the chess rules.
Please post solutions only in white text! Prizes await you in the afterlife ...... More Xmas puzzles on the Christmas problem-solving competition by Rocky64.
A. White on move. Black takes back his last move and replaces it with another move which allows white to checkmate him on the next move. How?
B. About the next diagram with white on move you are told that it occurred in a game where white could have checkmated black on his previous move. Can you figure out how that was possible?