Is this position legal?

Bah. Too lazy for editing :p

lol

Correct, although that's #104, not #115. Well done anyway! (Plus it's impossible to be upside-down; not enough captures for the pawns to pass each other like that.)

For #115, after doing some thinking I'd like to ask something slightly different. For #115-1 and #115-2, which black pieces must be original (not promoted)?

44Qf4+! is mate in three. 

A very creative position and an interesting solution to get there.

Nice solution...

Yep totally possible!

One can make it a bit harder by putting rooks on h1/h8 and demanding that both sides can still castle. 

@Irontiger what the heck. :-) Still, 5 captures per side is just enough to permit the d-, e-, f- and h-pawns to get out of the way... but then the other pawns are gonna get in each others' way. So I say your position + stipulation is impossible (possible if just one of the sides can't castle.)

@11qq11 trivially legal. Black knights died on c3 and f3, then white puts the bishops and everything else in place while black does likewise... really not much to say here.

Note above, pieces are on the other side.

^ Illegal, pawns cannot pass each other without at least 8 captures total.

Well, the not-so-trivial thing is that you cannot promote on e1/e8, f1/f8 or h1/h8 if you want to keep the castling option, hence the closest where the kingside pawns can promote is the g file. But the players cannot both use that file...

The queenside is easy to do with only a few captures.

OK, next. With or without the pawn on b5 :

d1/d8 is also off limits. Which is way too many captures total in any case.

For your above puzzle, there are 3 things immediately notable: (white text, white text)

- White's in check so black moved last. Withdraw Bx(w)e6 and it gives white spare moves.
- Now the white king's in a strange place, and he must've wandered in via most of black's back rank, entering via a7 or c7.
- Black's light bishop used to be so cute when it was a pawn.

Now black's light bishop must have been promoted on h1 or f1, coming from c7 (the a7-pawn can't reach) and made 5 captures, the ...Bxe6 makes another, and the b5-pawn (if it's there) totals 7. White's missing 2R, 2N, KB and the g-/h-pawns make 7 pieces so we're good. (h-pawn could've promoted; c1-bishop can't have moved.)

Then everything is clear. We have a method to construct: c1- and f8-bishops die, white suicides everything to a berserking c-pawn (g- and h-pawns make 3 captures and promote on f8), black plays a6, white's queen and king dive in (from b6), ...axb6, ...Bxe6#. Legal with and without b5-pawn.

You just cooked my solution ! Congratulations !

I miscounted the missing e6, and thought g and h could not be used as food as "they have to go both (false again) beyond g3 and h2 to let the rook go through", so that in my mind there was not enough food for a b5 foot soldier. 

is this legal

yes

What about this??

^ Again, trivially legal.

Tip for those who would create puzzles: The difference between a tricky puzzle and a trivial puzzle is not how outlandish it looks, but how difficult it is to construct. Irontiger's puzzle is a good example, with several features often used in retros:

- Doubled pawns indicating captures.
- Unusual positioning of pieces requiring some thought as to the last moves played.
- Pawns on the second rank are an "absolute barrier" that must not have moved.
- Total number of pieces missing and captures required indicating promotion happened.
- Bishops remaining on their colour meaning some captures are impossible, or indicating underpromotion.
- Knights necessarily having capturing pieces on their starting squares (e.g. the f8-bishop, to allow promotion there.)

Weaving these elements together make for tricky and interesting puzzles, as these features usually suggest a specific sequence of strange happenings to get to the final position.

P.S. @Irontiger, put a white bishop on f8 and it should be uncooked. :D