Originally posted by SwissGambit
No, there is a far better way to solve it. Look at what Willzzz is doing.
Let's focus on the proper method for solving.
1) Count the stuff on the board, identify missing pieces, and count the pawn captures.
White has 14 pieces on the board. He is missing two pawns.
Black has 13 pieces on the board. He is missing two knights and one pawn.
Armed with this knowledge, look at pawn captures. Just pick the most likely captures and count them. Do it using as few captures as possible.
White made two captures with the a7 pawn to get around the black pawns.
Black made two captures. The d pawns are doubled, and there's already a pawn on e5, so two captures must have been made to get this structure.
That means we've accounted for all but one of the missing pieces. Let's say d4 and e5 were originally on e7 and f7. Which black pawn is missing? Has to be the g-pawn.
How were the two white pawns captured? They were probably the f- and h-pawns, so they couldn't have been captured directly by the black pawns. Therefore, the black pawns must have captured pieces. How are they able to capture pieces when white already has the full set of 8 pieces on the board? Answer: white must have promoted two pieces. Something had to promote to either a) replace the pieces that were sacrificed to black pawns, or b) sacrifice themselves to the black pawns.
Of course, Willzzz has already come to this conclusion, but I thought it might be illuminating to show how one reaches the conclusion.