Solution to The Cultural Exchange Puzzle

"Elementary, Watson," was Holmes' reply when I asked him how he could possibly have ascertained so much about the game position from The Cultural Exchange Puzzle that his brother Mycroft and I had presented to him.

"I will not bore you with the details, which surely you can deduce for yourself, Watson, but the solution begins to make itself apparent when one considers how any non-Russian power could possibly position two fleets in St. Petersburg and Sevastopol within the first seven turns of the game.

"As our mutual friend Rick Desper remarked after I left you (for I was indeed rather amused by the position, and I presented it to him for his pleasure), a simple glance at the board is sufficient to determine that the only power with the possibility to move fleets into both of the two Russian ports in the first seven turns is Italy. We could quibble about the fleet landing on the north coast of St. Petersburg instead of the south, but your information stated only that the units obtained positions in the same centres, and obviously it is impossible for Italy to reach the south coast of St. Petersburg in time. Only the Atlantic powers can do so, and as we have already asserted, they are ruled out by their distance to Sevastopol. Ergo, Italy must have sent a fleet to the north coast of St. Petersburg, and thus must have been played from the beginning of the game (in your game that was so riddled with absentee powers). Further, he must obtain a build to enable him to maintain four units. The moves of the Italian armies to Warsaw and Moscow are obviously possible in the time allotted.

"Since Russia is being occupied by Italian units, Russia is certainly one of the powers shuffling to occupy different foreign home centres, and we know that while doing so, she must lose a unit. Our attention now turns to the possible final positions for the Russian units. The difficulty here is the fact that so many powers were unplayed, so the destination for the Russian units must be a power to whom travel is possible without undue interference from the units in civil disorder.

"Equally important, we must keep in mind that the units originally at the destination of the Russian units must shuffle into other home centres as well, so a considerably wide travel path would seem to be necessary.

"Compounding this is the fact that wherever this power's units are going, the units originally there must also be moving to reshuffle. We know that one power is moving to Italy, and given the need to avoid territory in civil disorder as much as possible, we can further conclude that at least one of the powers must avoid moving through the same corridor as the other two or three.

"This leads us to consider, for their proximity, Austria or France as owning the units which move to Italy.

"As a matter of fact, Watson, I am very near the end of my explanation. It remains only to conclude from the ample evidence that your Russian units moved to France, the French to Austria, and the Austrians to Italy, from whence, of course, went the units that took possession of your own home centres. If you'll step to the Diplomacy table here, I will show you how the moves in your game must have transpired."

With that, Holmes quickly set up the board and took me through the moves of the game, season by season.

Needless to say, Holmes was entirely correct. However, I had one more question, which I was sure would trip him up. "Holmes," I began, "while you reached the correct conclusion, it seems to me you started your explanation assuming more information than I had initially given you."

"Indeed, Watson? Have I? How so?"

"At the bar in the Calhamer Club, Holmes, I am positive that the identities of all four shuffling powers were not disclosed to you. But you began your explanation by determining which power could shuffle into the Russian centres. You were obviously using the fact that I later disclosed to you that I had played Russia. Without that knowledge, it seems your explanation proceeds from an unmerited assumption. Had I not told you that I had played Russia and lost my two ports, you could not have solved the puzzle."

"And yet I did, Watson. And, if you'll recall, so did my brother Mycroft. Your disclosure that you played Russia informed me of nothing at all save that fact. Already I knew that someone had played Russia; this follows just from the information you had presented. For you see, Watson, the rearrangement we've been discussing is the only possible one that allows four powers to reposition themselves under the constraints you described to me. It took me but a mere second in the bar to eliminate all other possibilities than that the four powers in question were Italy, Russia, France, and Austria."

With that, Holmes excused himself to tend to his botanical pursuits, and I was left, once more, in awe of the great intellect with which I shared my apartment.