solve this

easy

1        nc7ch

Qxc7! Also Qb8+ Kxb8 

There's no good solution, since the position is impossible. 

There are several problems with this position, only some of which can be solved by unlikely pawn promotions. 

Black's light-squared bishop can only be due to a pawn promotion, since its original position is still penned in by black's own pieces. 

A bigger problem is black's pawn on b6, which requires an unlikely string of moves and promotions (since white cannot have lost a pawn on b6, but only white pawns are missing).

The position might be possible, but the whole puzzle just smacks of pieces thrown on the board without thought. It seems safe to assume the solution is just as confused. 

Hairhorn is right! The white queen cannot reach the e5 square. Neither the c, d nor e pawn have moved...

I was so caught up in the details of Black's position that I missed this obvious problem with White. 

The queen could have been captured by a knight, then replaced by promotion, but the sequence of moves to get there is so unlikely I haven't bothered checking if it's in fact possible. 

Lol. Considering black's given material, it's very difficult to believe white had any chance of promoting its pawns...

Yeah, Black would have had to move pieces away from, and back to, their start positions, and casually let more than one pawn promote. At this point I am just considering what is possible rather than what is likely, since none of this is likely. 

It's quite unreasonable to attempt so, since the actual position isn't legal

There's a whole thread devoting to debate and proofs that given positions are legal or illegal, it's quite interesting ("Illegal Position Contest" in the "Fun with Chess" category).

This one is probably illegal, but the proof that positions are legal are often easier (since they are just games). 

I know this one! It's great indeed!

But there's no reason moving the debate there. It's clearly illegal...

The position is legal.  I assumed that this is a type of puzzle known as a "retro" (for "retrograde analysis").  Since I saw no definitive reason for the position to be illegal, I figured that "solving" it would be to create a proof game, such as the one above.

Note that, since we were not told whether it was white or black to move, I created the proof game to have either result.  The position after move 38. Ng1 is identical to the final position with the exception  of which player has the move.

Yes, the moves are clearly nonsensical. But the point of retros is not to show the best moves, but rather to show what is *possible.*

Now, if we add a stipulation that castling for white is still possible, then it would require a different proof game.  In that situation, white's queen would have to be captured on her home square by a black knight and one of the white pawns that were simply captured in my above game would have to promote to a queen.  So, even if white still had queenside castling privileges, the position would still be legal.