Is this position legal?

443 is not trivially legal. I was able to tell at once that it is illegal. Try and find out why!

#442 is nice. I like it. A good introductory problem.

#443 seems trivially legal to me. Black is missing enough pieces, he can retract a white capture... no issues.

#450 trivially legal with promotions.

#451 trivially legal after retracting the simple trickery of the last move.

@falcogrine: It's definitely OK to struggle a little with the problems at first. Especially when there are even 2 or 3 retro motifs, which take a while to get used to. Stuff like cross-captures (basic yet sneaky), promoted pieces suiciding or replacing original pieces, and trapping pieces in cages are almost the bread and butter of retros.

For composing, personally I find it easiest to start with a cage (like the lower left of #287/322, or the trapped bishop motif I got from Smullyan) and then build up from there, trying to work in more and more complex sequences of events in. At every stage pausing to properly solve the prototype to check for cooks, of course.

Google is your friend for finding retro resources. Including simple introductory problems. Classic short (<8.0) proof games are a good way to see individual themes in action.

Finally, a little problem. It contains a few simple ideas, then I decided whatever, let's see if we can't get it looking as pretty as possible too. :P

People! #443 is illegal because the white pawns cannot all be so far on the king side! There are 5 pawns on the g and h files all before rank 6. An imposibility in any case!

Hmmm... White bishop, maybe queen taken on g6 after knight in corner. further than that is guesswork by me. black d pawn promotes on a1, taking rook. black knight to h1, then g2, which lets the bishop out. this would be have to be before the knight goes to h8. The black king would have to come in g2 through h3, then pawn goes to h3, king goes to h2, bishop works its way in. Am i close?

I'm going to disagree on this one. For example, pawn on g5 came from d2. Pawns on g2 and g3 come from e2 and f2. H pawns come from g2 and h2. Of course, there are other ways to arrange them, but that looks pretty easy.

Ahhhhhhh you're right! Apologies! My brain counted squares and said the wrong thing... lol move on with your lifes people nothing to see here!

Needless to say, I don't think a real game ever has or ever will be played that way....  :p

I've done that too for far too many of these!

On the same position, I thought it was impossible because I couldn't see any moves to retract for white...

Hm. Not close, but it's the obvious first try. Perhaps try counting how many captures black has made. Then once you've done that, see which white piece could've died where. That should highlight some things.

The best way to see if you're close is to try and construct a proof game from the starting position. This will ensure that any bits of trickery will become impossible to ignore. In fact, doing so is the best way to solve problems until you're confident enough to just play retromoves to reach a legal position.

I'll keep working on that position. For now though, I have to call it a night. I hate these timezones.

I PM'ed the solution to #453.

46.0 and 45.5 solutions. And virtually immediately too. Both of you are very strong.

So it's only fair to throw out another challenge, assuming it's not cooked. Is the position legal? What about without the wBf1?

how does the white queen get there without the black king already being in check?

The last move is a7xb8=Q+.

I don't see how a pawn could get to a7 in the first place

a7-a6, b2-...-b6xa7xb8=Q+