Here are a few more reconstruction challenges. How did this happen?
First a simple one. I believe I took less than two minutes to solve it blindfolded (or at least without a board):
1) Black's 4th move is 4...Re1+.
The next one I believe is harder. But I may be mistaken, as it was one of the first I tried to solve:
2) White plays the moves 1.f3, 2.Kf2, 3.Kg3, 4.Kh4. Black's 4th move is to give mate.
The last one probably is the hardest. Some 15 years ago we were three players trying to solve it, one of us a future grandmaster. It turned out that it was the lowest rated - a 1700-player - who showed up in the chess club the next evening with the correct solution:
3) A game opens 1.a3. White's 5th move is to give mate with a rook.