Mutual Aid

During the rebuilding after World War II, we were short of tractors. The machine and tractor stations would lend each other equipment as needed.

Three machine and tractor stations were neighbors. The first lent the second and third as many tractors as they each already had. A few months later, the second lent the first and third as many as they each had. Still later, the third lent the first and second as many as they each already had. Each station now had 24 tractors.
How many tractors did each station originally have?

(Source: The Moscow Puzzles: 359 Mathematical Recreations by Boris A. Kordemsky, edited by Martin Gardner)

Initially, I was confused by the wording. But what it really means is that, at each time step, the lender station doubles the number of tractors that each of the two lending stations had, and subtracts the total number of lent tractors from its own stock. Like the very first puzzle I ever solved here, this can be solved backwards easily.

At the final time step, all stations had 24 tractors. In the previous time step, the third lent the first and second as many as they each already had. What this means is that in the previous time step, the first and second stations both had 12 tractors, and the third lent 24 total to the others. The three stations then respectively had 12, 12, and 48. Repeating this process again for the previous time step: 6, 42, and 24, and for the earliest time step, giving the final answer: 39, 21, and 12.