A short article described how the magazine's problem editor, A.J. Fink, walked into a storage room and picked up a copy of Berliner Schachzeitung from March of 1912. That afternoon there were a number of strong players hanging out at the Mechanics Institute and they set up the position in the diagram.
The position was from an actual game and Berliner Schachzeitung was offering a prize for anyone who could find a win for white. The guys at the Institute came up with 1. Qxf7 Qa5 2. b6 (The threat is 4.Rxe3+ Bxe3 4.Qc7mate.) Qxb6 3. Bb5 as their solution, but the next day a master named Charles Bagby came up with 3...e5 and nobody could find a win. Fink was unable to locate the issue that contained the solution, so they remained mystified as to how white can win and they were offering a book prize to any reader who sent in the right solution.
I let Stockfish analyzed this position for about a half hour and discovered that there is no win, but the position is amazingly complicated; in some variations there is only one move for both sides that avoids losing. It would be interesting to know if any readers, either in 1912 or 1950, discovered what they thought to be a win.