"I understand now, Holmes, how you determined which power was eliminated, and which power elected to play 1902 without any units. I also understand how you were able to deduce which power was played by the Sultan and which was played by the refugee. But now, Holmes, how did you determine the code-word to tell our friend the refugee? I'm afraid I'm still at a loss to proceed."

"Well, Watson, as I recall, you did detect the question that was being asked us by the Sultan; correct?" Holmes asked casually.

I had, of course (with a little help from Holmes), determined the manner in which the question was being asked. "Yes, Holmes," I said rather proudly, "it was cleverly hidden in the written account of our refugee's escape from the Sultanate. By ignoring all but the initial letter of each sentence, I found that it spells a question! 'Where is Army Brest?'"

"Indeed. That is the question the Sultan asked, and I simply relayed the answer to his trusted servant." Holmes made a move as if no more explanations would be necessary; he apparently intended to retire and read, but I stopped him.

"Well, Holmes, where is Army Brest?" I demanded. "I assume that the Sultan is asking where the army that was built in Brest at the beginning of 1902 ends that year, yes?"

"Yes, Watson. And that location is the answer to his question." This time, Holmes actually took a book from the shelf, but I was certainly not ready to let him leave me in my mystified state.

"Holmes, might I impose on you to show me how it is possible to determine where that army ends up?"

I expected that Holmes would be a trifle annoyed, but instead he simply smiled and walked over to the table where the Diplomacy board was waiting for him.

"Let us begin at the end. Russia has one centre more than France, the other powers all being eliminated. By 1902, France can have a maximum of twelve centres, so at most twenty-five of the thirty-four centres are owned. Since there are twenty-two home centres, only three neutrals can have been captured. In 1901, it seems that all twenty-five centres were already occupied (the unit counts are two, three, six, zero, three, eight, and three, which sum to 25). And the builds tell us that all three French and four Russian units have captured centres.

"One of the three neutrals that was captured must be Sweden -- it is the only supply centre accessible to Russia's St. Petersburg fleet.

"How are the Germans eliminated? Kiel can only be captured by convoy, and with the Kiel and St. Petersburg fleets committed (to assisting in the acquisition of Kiel for a foreign power and of Sweden for Russia, respectively), only Warsaw can take Berlin.

"Now let us consider which units were involved in dislodging Austria: eight units can move adjacent to Austrian units in Spring of 1901: Marseilles, Munich, Berlin, Moscow, Sevastopol, Ankara, Constantinople, Venice and Rome. (Warsaw, of course, we have decided is commited to taking Berlin.) Of these, three can only effect a dislodgement in Rumania. Additionally, we should note that all Russian units take a new centre and Rumania, and that Rumania is the only remaining supply centre reachable by Moscow. Thus, we know that the Moscow army must move to Ukraine and thence to Rumania, and it must be supported into Rumania by the Turkish fleet in the Black Sea."

At this point in Holmes's narrative, I nearly interrupted him to burst out with, "...or by the Turkish army in Bulgaria, of course." However, Holmes was on a roll and there was no getting a word in edgewise. He rushed on.

"Russia's Sevastopol fleet must end up in a supply centre -- with Rumania spoken for, we can now see that it must be Ankara.

"So the second of the three neutrals taken must be Rumania, from where Austria's army that began the game in Budapest is finally dislodged.

"To determine the final occupied neutral we must recall that most of Russia's units were landlocked after 1902. He must have occupied five landlocked centres, and moreover cannot have captured one from France (that is, he may not capture Munich or Paris). This leaves Serbia, Budapest, Vienna, Warsaw, and Moscow. Serbia is the only neutral on this list, and in 1901 only Turkey (with his Constantinople army) can occupy it."

(I now understood why the support for Russia's take of Rumania had to be with the Turkish fleet. I was glad I hadn't spoken up.)

Holmes continued. "Now, how can France get three builds without capturing a neutral centre? There is but one possible way: Brest must capture London, Paris take Munich, and Marseilles capture Venice.

"In turn, then, to remain at three centres, England must capture a non-French foreign home centre: there is only one available, Kiel via an Anglo-German convoy (recall that we had already deduced that this would occur; however, we now know that it is an English, not a French, army which convoys in to Kiel).

"Similarly, to remain at three centres at the conclusion og 1901, Italy must take an Austrian centre. And of course, to be eliminated as required, he must lose that centre to Russia in 1902. Given that Russia's forces end up landlocked, this centre must be Vienna.

"The demise of Italy in 1902 provides further information. In particular, the demise of Rome and Naples. One of these can be taken by the army which starts the game at Marseilles, and the other can be taken by army built there at the end of the opening year. This, however, can only happen if that army is convoyed to Tuscany in Spring of 1902 by the Italian fleet. Therefore, we know that Italy must order his fleet to the Tyrrhenian Sea in Spring of 1902, and it must be used in the Fall to convoy a French army into Tuscany.

"And thus, the centres held in 1901 are clear."

My mind was racing, but believe it or not, I think I was keeping up with my friend.

"In 1902, Russia must occupy Serbia, Budapest, Vienna, Constantinople and Smyrna. To do this, she must use her Ankara fleet and four armies (those that, at the conclusion og 1901, were in Rumania, Warsaw, Sevastopol, and Moscow). The Moscow army must be assistedn to Constantinople by a Turkish convoy across the Black Sea.

"At the same time, France must capture Rome and Naples (as I have previously discussed), as well as Edinburgh and Liverpool. Getting another French units into England (Scotland, actually) requires cooperation of the English fleets, in both the North Sea and the English Channel. Brest and Paris must both be convoyed, but to where? Paris can only be convoyed to Edinburgh in the Fall, and for Russia to take an English held centre (to assist in the elimination of the Englishman), the Russian must go to Kiel. Where, then, does Brest go? Ah, this is the Sultan's question, isn't it? There is only one option -- it must be convoyed through English Channel and the North Sea to Norway in Spring, then it must move into St. Petersburg in the fall!

"Finally, Russia can only build two armies in 1902 (he builds wherever he can, yet he may only have one more unit than France, who will have nine). Obviously, Russia cannot build in a French-held St. Petersburg, but one other home centre must be occupied. There is but one way to do this -- his army that took Berlin in 1901 must have returned to Warsaw in 1902!

"To be quick about it, Watson, here is a set of moves that meets all the criteria described in the refugee's story. There are other move sets, where the units take different paths but to the same destination or where units just have to stay out of everyone's way and out of a supply centre, but the results, of course, are the same."

With that, Holmes proceeded to move the pieces on the board around and describe his movements as he did so. I reached for pen and paper and was able to capture his efforts. These are reproduced below:

After concluding the first game year, Holmes inhaled deeply from his pipe and stared hard at the board in satisfaction, then said, "Notice, Watson, that England, Italy, and Turkey each have three units and three supply centres each, thus no need to order builds. Germany has no supply centres whatsoever; therefore that player must disband all his units (which again requires no explicit orders). Only Austria, France, and Russia need to issue orders in the adjustment phase, and obviously Austria is the one, who (despite having no units), elects to waive his builds. We know that France and Russia build only armies, so we know the starting locations of all units for the next year."

With that, Holmes added more Russian and French armies to the board, and removed the German units. He thereupon started moving the pieces around to illustrate the second game-year.

Satisfied once more, Holmes gestured around the board while he pointed out, "Thus, Watson, all conditions in the description are met. All powers but France and Russia are eliminated, France owns twelve supply centres while Russia owns thirteen (that is, as the requirements stated, Russia has one centre more than does France).

"At this point, as required, all powers build as many armies as they can possibly build. France builds three while Russia, having only Sevastopol available in which to build, builds but a single new army. Thus, to begin 1903, both Russia and France have nine units.

"Russia took one supply centres from each of the eliminated powers: Budapest from Austria, Kiel from England, Berlin from Germany, Vienna from Italy, and Ankara from Turkey.

"Finally, five of the nine Russian units (Moscow, Warsaw, Serbia, Budapest, and Vienna -- the 'majority,' as called for by the Sultan's puzzle) are landlocked."

Satisfied that I could possibly ask no more questions of him (and he was right; my head was spinning!), Holmes settled down with his book and we didn't speak of the Sultan the rest of the evening.

-- Dr. John H. Watson

via Graeme Ackland and Robert Rehbold
(gja@ph.ed.ac.uk)

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