There are actually two variants of the "obvious" solution.

1) How long time until the crash? 200/(50+50) => 2 hours. Two hours at 75 mph -> 150 miles.

2) How long for the train to run until the crash? 100 miles. How much faster is the fly? 100*(75/50) = 150 miles.

Note that the infinite series I mentioned in my previous post is a simple limes function, and can quite easily be solved. limes 1/(5^n) for n=0 -> inf solves to 1.25. The first run for the fly is 120 miles (200 miles * 75/(75+50)), and 120 * limes -> 150 miles.

Yes, if von Neumann was good with math, then he would have been able to both set up and solve the limes of the infinite series in his head, since the solution has a finite (and very low) number of steps.

Yes, I would probably be able to set up and solve the infinite series in my head, but I'm way softer than von Neumann so I would need much more than two minutes, and it might leave scars ;)

In math, an infinite series need not represent a problem, if it approaches a fixed value when you keep adding. The above is a quite easy series, but it takes a bit of thinking to see the series in your head. This is also a reason why a software developer must always look several times at a problem, and not immediately jump for the "obvious" solution.

Another fun thing: How fast can you sum 1+2+3+...+99+100 in your head? Or on paper?