More Hints for The Dead-Letters Affair

"It is quite elementary, Watson! To begin with, you surely see which type of units (armies or fleets) must be at the ministers' locations. Given the three clues you placed at the end of your list, they could only be armies, since every fleet in any set of two can obviously reach the other's location in exactly the same number of moves. (Except the fleet at St. Petersburg, of course -- many non-Russian fleets could reach the north coast before the Russian fleet from the south coast could make the reverse journey. However, as you surely see, other requirements of the Sultan's letter rule out this possibility.) Since this much was doubtless already clear to you, this certainly is not the next deduction that you are seeking."

I just nodded silently (I had not made the deduction Holmes had recounted, but now that he had explained it, that much did seem, as he said, elementary).

Having determined that I wished to proceed beyond that issue, Holmes continued. "Simply think about what your final three clues there are telling you about the number of moves it takes each minister to reach the other. Surely you can see precisely how many moves the trip takes in each direction."

Surely I didn't. After a few minutes thought, however, I understood what Holmes was saying. Those three clues did indeed tell a lot about the travel time not only from each minister's location to the other, but from each to the Sultan's site! They specified that one minister could reach the other faster than he could reach the Sultan, but that the other minister was in the opposite situation (able to reach the Sultan quicker than he could reach the first minister). Combined with the fact that both ministers could reach the Sultan simultaneously, I was able to conclude much about the locations!

Obviously, the two ministers were not in adjacent locations (such as Munich and Berlin), for then each would only take a single move to reach the other's location.

I then considered whether the shorter trip could be a mere two turns in length. A bit of investigation and thought showed me that if an army (at the outset of the game) can reach another's location in two moves, the longest it could take to make the reverse trip is only three moves. For example, the army in Budapest needs only two moves (and aid from a Black Sea fleet) to reach Constantinople, but the army at Constantinople requires three moves to reach Budapest when the game begins.

I had just set out to determine whether the ministers could indeed be located at such a pair of locations (that is, a pair having just such a "two moves in one direction, three in the other" relationship to each other). Something in the back of my mind was bothering me about this possibility, but before I could lay my finger on it, a messenger from my office arrived and I hastened to dress the wounds of an accident victim. I did not get back to the Sultan's puzzle until the next day.

Chances are pretty good that no hansom cabs have just overturned in your neighborhood, so while Watson tends to the injured, you are free to finish what he has started. When you have done so, make sure to mail your answers to The Pouch!

Back to the puzzle....