King Bleme from Paris decides to have a meeting with King Duister of Amsterdam. The distance is 751 kilometers, and the retinues of both kings start at the same time. The French king travels at a pace of of 15 km/h, the Dutch king at 10 km/h, with the idea of meeting somewhere near Brussels.

Quick messengers travel back and forth so the kings can be entertain themselves by means of letter chess while they travel. The messengers canter at a pace of 30 km/h. The game ends when the kings are within one kilometer of each other. Each king makes a move immediately, by resorting to a library of conditional moves, so there is no unnecessary time loss.

How long is the distance travelled by the messengers?
How many moves are played?

The number of moves is a tricky one. The gap closes at the rate of 45km/h one way, but 40km/h the other. The number of moves will differ depending on the point at which the messenger starts. As the gap between the Kings gets smaller, the messenger will get very busy, assuming an instantaneous transfer of information (i.e. move and counter-move). I think there will be 4 moves in the first 29 hours, but I'm not sure about the last hour. However, given the move sequence {1. f3 e5, 2. g4 Qh4#} there is no 5th move. Problem solved! ðŸ™‚

That's why I made the game from 751 km to 1 km, rather than 750 km to zero, avoiding the near-infinite games.. of course, the black checkmates white in two moves also handles the problem nicely. ^_^