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Sherlock Holmes,
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The Colonel and I slapped Holmes on the back, saying, "Good show!" My friend had begun to enlighten us concerning his resolution of The Missing Master's Mystery, building on the hints that he had provided. Holmes was enjoying the attention, and his pipe. After a brief pause, he said, "without proceeding further, we cannot yet say definitively whether armies or fleets entered Picardy, Tuscany, or Piedmont. In order to determine the answers to these questions, as well as the rest of the board position, we must take evidence from more of the facts that the Captain left us." Holmes nodded seriously, and asked, "Shall we proceed?" I was excited to continue, and felt better prepared than at the beginning of this puzzle, but I realized that there were still an enormous number of variables. Which neutrals were captured in 1901? Who captured them? Where are the remaining pieces on the board beyond the 12 that we know? Sensing my anxiety, Holmes quietly spoke. "Here, my dear Watson, we might begin working backwards. As I mentioned, the case of France might make a good example. We have several scraps of information about France, which might be applied to our advantage. Let us one more time review the facts the Captain left for us, shall we?"
First and foremost, we know that France must have been positioned to enter both Tuscany and Piedmont in the Fall of 1902, from the Gulf of Lyon and Marseilles, respectively. Now, there is an interesting fact regarding particularly an attack from the Gulf of Lyon. You see, according to Fact 2, France cannot have built a fleet in Marseilles. We can deduce from this that the fleet that finds itself in the Gulf of Lyon must have come originally from Brest, where France's fleet begins the game. Even taking its shortest route, it would require exactly three tempi to travel to the Gulf. That fleet must have gone to the Mid-Atlantic Ocean in Spring of 1901, to the South Coast of Spain in the Fall of 1901 - thus securing Spain as a 1901 neutral for France, incidentally - and then to the Gulf of Lyon in the Spring of 1902." "Brilliant, Holmes!" exclaimed the Colonel. "Why don't you just place the fleet on Tuscany for Fall and consider another of the invasions solved?" "Not quite yet, my good man," replied Holmes. "For the invasion could have come by convoy from Spain, via the Gulf of Lyon. It is too soon to say." "Quite right, Holmes," nodded the Colonel approvingly. "However, I would point out the tremendous amount we have learned from the knowledge of the movement of this single French fleet. First, as I mentioned, the fact that the fleet had to move to Spain in the Fall of 1901 not only demonstrates that France is Spain's owner and gained that player at least one build, but it also tells us that the Italian fleet was not in the Western Mediterranean in that same season, or else they would have seen each other. We can note that for later analysis. Next, it informs us of where the other French units might have moved. With our most recent discovery in mind, there is another conclusion that we must draw about the invasion of Piedmont. Can you see what it is?" The Colonel and I each considered Holmes' inquiry. He spoke first. "It had to be an army, Holmes! The invasion came from Marseilles, and even if France had built another fleet in Brest during the '01 adjustments, it never could have reached Marseilles in time!" Holmes looked pleased as he placed a French army on Piedmont. "Excellently done, Colonel. But there is even one other subtle detail that we can conclude from this chain of events. You see, as we have already identified the units that have held, we know that every other unit on the board has moved each and every turn, and has never stood off. This is a critical fact. This means that a French army must have moved in to Marseilles in the Spring of 1902, so that he could move into Piedmont in the Fall. Where could that unit have come from? Spain or Gascony only, as Burgundy cannot be traversed without tipping off the German. Aha! But Spain, as we already know, was occupied by our fleet at the beginning of that season! It must have been Gascony. It starts to come together here." I was confused, so I wrote out the orders we knew for France, season-by-season.
Holmes consulted my list and nodded emphatically. "Those are the moves most elementary to conclude. But what of the other units? In the interest of time, I shall suggest to you the only two possibilities that are consistent:"
"Dear God, Holmes, how did you arrive at those choices?" I asked. "From a careful analysis of all of the facts in play, as well as what I myself have deduced about the English and German moves. A better question to you, Watson, might be 'How do we choose between these self-consistent possibilities?'" "How, Holmes?" I asked, now thoroughly lost. "It might be revealed by consulting Fact number 1. More than one power, the Captain tells us, built more than one new unit in 1901. If there is only one other power on the board that we can conclude definitely built more than one unit, then we must agree that my first alternative is better. If, on the other hand, we find at least two others who managed to secure at least two neutrals, then we are unsure again, so perhaps a good way to proceed would be to try to determine which neutrals could have been captured, and by whom, in 1901." I frowned with concentration. "Well, Holmes, I suppose I could give it a try..." Holmes proceeded: "But before worrying ourselves too much more with France, perhaps we should turn our attention to the Balkans, where we might apply some similar logic to the case of the Austrian, the Turk, and the Balkan centers. The Austrian, you may notice, is extremely restricted in his early moves. With his fleet in Trieste standing still until the Fall of 1902 when he enters Venice, the player is highly limited in the spaces he may visit without alerting another player. Any move to Galacia or Rumania will tip off the Russian, and any move to Tyrolia will certainly alert the Italian and the German. Given that he moves his armies every turn, we can conclude only one thing: That his Spring moves were Budapest to Serbia followed by Vienna to Budapest. Agreed?" I nodded hesitantly. "Good then!" Holmes continued. "Then we already know something about the Turk, as well." Slowly, Holmes' logic becan to sink in. I interrupted him, stating excitedly, "The Turk did not open to Bulgaria!" Holmes looked pleased. "Indeed, Watson. Quite unusual for a Turk, but true nonetheless, for if Austria was present in Serbia, he would certainly have noted a Turkish unit in Bulgaria, and been noticed in return! From here, though, things become less certain. In my opinion, we now have five options for the Austrian moves, each carrying with it a unique set of limitations. His armies could have continued on boldly to both Greece and Serbia, shuffled to Albania and Serbia, split between Greece and Vienna, or Albania and Vienna, or fled ignobly back to their starting positions. Which was it? Perhaps the Sultan's strategy can provide us with answers... "The Turk did not move his army in Constantinope to Bulgaria; on this we are agreed. His only two choices for it then were Ankara or Smyrna. We can rule out Ankara, for that province's fleet must have moved to Constantinople, as Armenia and the Black Sea were off-limits. Ah!" Holmes said, as if he had just realized something for himself. "There we are, then. Ankara to Constantinople, and Constantinople to Smyrna. As for Smyrna, either Syria or Ankara will do... we shall leave that question unanswered for now, but as I suggested before, when trying to decide between two destinations for a unit, you would do well to select the one that has not yet been visited. Let us claim that the army in Smyrna moved to Syria for the time being, then. We are now left with this position for Austria and Turkey before Fall of 1901:"
The Colonel snorted. "Not exactly a wealth of information, Holmes. A mere one season's information, and not even complete." Holmes cleared his throat. "I disagree, Colonel, for this has given us several facts that we might use down the line. First of all, we can see from the Turk's positon that he now cannot possibly attain more than a single build in 1901, and then only if he moves to the south coast of Bulgaria with his fleet in the Fall. If he did that, then we know that the Austrian cannot have built at all, for he cannot have been present in Serbia or Greece while the Turk was in Bulgaria. Conversely, if the Austrian gains either Serbia or Greece, or both, the Turk would have made no gain at all. Thus, in addition to that more immediate information about the two powers' units in the Fall of 1901, we also know that we can rule out the Turk as one of the powers who did not build more than one unit in 1901 (and, if he built one, then we can also rule out Austria.), thus getting us closer to resolving the question, 'to whom was the Captain referring when he wrote Fact number 1?' "Additionally, there is another clue, when added to information we already have. If we wish for the Aegean Sea and the Eastern Mediterranean to have been visited by the Fall of 1902, we know only the Turk could visit them. Therefore, the next moves of his fleet might well be to those spaces, and, to reiterate, we should always prefer moves which allow us to visit unvisited spaces to those that do not. Perhaps you are right, Colonel, for at this point we cannot yet say with any more certainty what the exact moves of those two powers were, but, as you shall find, each detail counts." "You see, my friends, the same logical steps can be applied toward every region of the board. Simple analysis of all possible moves by every power will reveal a very limited number of possibilities which hold true to all of the facts. The method that I applied was to simply determine the moves of which I could be certain for every power. When I reached a point when I could not be certain of a power's moves, I would return to one I had already examined and attempt to fill in more moves armed with my new information. For example, as I mentioned earlier, when I discovered that France had to to have a fleet in Spain at the end of 1901, it also demonstrated to me that Italy could not have been in the Western Mediterranean at that time. Or that Turkey and Austria have a variety of mutually exclusive moves! Deductions such as these, combined with the lists we generated earlier showing spaces that could not be entered, as well as spaces that could only be entered by a single power, resolve the bulk of what might seem at a glance to be ambiguities. One might simply make a grid with five columns, one for each of Spring, Fall and Adjustments of 1901 and Spring and Fall of 1902, and fill in the locations of units as they are discovered. It is worth restating at this point that we must never forget that every unit (excepting Sevastapol, Trieste, and Venice, as we know) moves, uncontested and unsupported, every turn. We will see that in many cases, there is only one choice as to how that unit is able to move." Holmes paused thoughtfully for a moment. He continued: "However, what I believe might have been the Captain's greatest gifts to us, and the one you will see are absolutely crucial to the final resolution of this mystery, is Fact number 8. Fact 8 tells us that there are a mere four spaces on the entire board that had not yet been entered, and each could be entered by a fleet on the very next turn! In many cases, when unable to decide between two moves for a particular unit on a particular season, I chose for that unit entrance into a space that had not yet been entered. I actually reached several complete solutions to this problem which held true to every fact except that one, but only one solution that held only four spaces unvisited. Once bound by this limitation, the options became very limited indeed." "Finally, Fact 9 deserves a bit of discussion before we go on to generating our grid. Once again, this fact is useful when attempting to decide between self-consistent possibilities. Knowing that all units have to end away from a power's home centers, you will find, answers the rest of the questions you will have." The Colonel, who was engrossed by Holmes' observations, spoke up. "Well, then, Holmes. Let's get to it!" With a pen and paper in hand, he began drew the grid as we gathered around him. For nearly two hours, he and I slowly added positions of units as we saw them, taking care to keep Holmes' observations of the facts closely in mind. As he promised us, we ultimately discovered that there was indeed only one ending position for the entirety of the four seasons that matched the Captain's incomplete observations about the board:
"Why, it was elementary, my dear Watson," Holmes
concluded.
Dr. John H. Watson, M.D.
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