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Sherlock Holmes,
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Editor's Note: In our last issue, Holmes provided a solution to the difficult problem posed in The Curious Case of the False Start. Here he wraps up the loose ends, and puts the case to rest. Read on to witness the full cleverness of this master sleuth… Rocking gently on the rhythmic staccato of the wheels of the hansom cab rattling through the cobbled streets of London, I took out my notes to examine them for the peculiar facts that my friend Holmes had mentioned. It didn't take me long to discover a couple of them. Quickly scanning the pages I said: "Well, this is none too difficult. The unit that held for most of the game is the army in Constantinople after it moved from Smyrna. The province that was the scene of 3 consecutive dislodgements is Venice. France held all its units in the Fall of 1901, Italy in the Spring of 1902 and Austria in the Fall of 1902. As for the powers that kept their units inside their national borders, ..." Turning my head to face him, I noticed from the way he gazed at the ceiling of the cab and the smile on his lips, that his mind was somewhere else entirely. "Italy and Turkey," came his sudden answer. "From the look on your face I can tell that you thought I wasn't listening. Dear Watson, with some practice it's perfectly possible to completely masquerade one's mind with one's facial expression. It's one of these techniques that has been of tremendous use in my career." He smiled at my show of surprise. "Though I will confess that at present I'm more occupied with the prospect of this evening's experiment," he added. "It's just as well that you invited yourself to your old quarters. You won't regret it." "And what is the subject of this experiment?" I asked prudently, for I knew my friend's propensity to experiment with substances that tended to explode. "Why, the potted ferns, of course! But here is the house. Come on in and see for yourself." After paying the cab's fare I followed Holmes inside to the room that used to be my bedroom, but had now turned into a small chemical laboratory, complete with distillation columns, bunsen burners, a small steam engine and the like. There, on a table against the wall, stood a large glass case containing several exotic plants, dominated by a monstrous fern that spread its green leaf-shaped branches to every corner. "I see you're not immune to the fashions of the day," I remarked. "Those Wardian cases are quite popular nowadays, but I haven't seen quite one of this size. What have you been planting?" "For me it's not some little fancy like those of your well-to-do patients," my friend countered. "This is science, and practical science at that. With the invention of the Wardian case we are finally able to transport living specimens of flora and fauna alike from all over the world without fear for decay during the long and stormy trip aboard the vessels of the Queen's Marine. Imagine all the discoveries that can be made, the claims that can be verified of the extraordinary powers attributed to some of these plants. "I have tested and proven that this plant here is a tenfold more poisonous than our own endemic belladonna, while this root can be more hallucigenous than opium poppy, and this flower can attract with its scent a bumblebee from a hundred feet away and trap and devour it. But the object of tonight's pursuit is a more peaceful one." "I'm glad to hear that," said I with a touch of relief. "Have you ever heard of palimpsests? No? They are medieval manuscripts containing copies of classical texts, but later scraped bare of their texts so that they could be reused and turned into prayer books. I have here a single page borrowed from the Library of the University of Cambridge. It's said that the original text possibly contains heretofore unknown work from no one less than Archimedes, the most proliferous inventor of ancient Greece." Unfolding the manuscript and holding one side up in front of a candle, he continued: "The monks folded the original page in two and turned it sideways, so that the original text is perpendicular to the new text. As you can see, the scraping did not remove all traces. One can with some difficulty make out the first sentence in the margin of the prayer book. But the rest is mostly illegible. "We know that the Byzantine copyist who wrote the original text used a different ink than the Christian monk who wrote the prayers. That's where the fern comes in. This species' habitat is the Amazonian rain forest. Its latex contains a pigment that will affix itself to the old ink only and make it stand out. But the quality we are looking for can only be found in a mature plant. Look how thick the root has become." He took a knife with a blade in the shape of one half of a hollowed out cylinder, and made a fine incision in the root with the tip of the blade. The liquid leaking out ran down the blade and collected there before being transfered to a glass container. Using his magnifying lens he examined the almost transparent milky white liquid. "Beautiful. Now this needs to be distilled to separate the active component that we're looking for from the rest. Here, hold this in front of your face." He handed me a thick metallic plate, its sides curving upwards, with a thin rectangular slit above the centre covered with glass and a strap to hold it on the head. "It weighs like lead," I remarked. "It is lead," Holmes replied. "Solid lead. There's a lady physicist in Paris who postulates that certain reactions may produce rays invisible to the eye that can penetrate anything but the most solid structures and do considerable damage to the system. Radioactivity she calls it. This mask should prevent our brains from getting fried." There was no real comfort in the knowledge that if the experiment didn't explode, it could kill us in various other ways, but there was little point in complaining. I followed his example and put up the mask. Peering through the slit I saw him attaching the container to the distillation column, then turning on the bunsen burner beneath it, after which the column started to hiss and boil, the gas escaping through the downward slanting column. At the same time he opened the tap at the other end so that running water moved up the column to cool it down, condensating the gas back into a liquid with a considerably higher concentration of the more volatile component, which dripped into a similar looking flask at the other end. After a while the boiling stopped and the dripping became a trickle. Holmes turned off the burner, removed the first flask, washed out its contents, then switched around the two flasks and turned on the burner again, stoking up the heat higher than the first time. This process he repeated a few times until he seemed satisfied with the result. The remaining fraction was perhaps only a quarter of the original, the white color more intense. He again examined it with his lens, and shook the container. Slowly so as not to spill a drop he then poured it into a pipet. "We may remove our masks now. Notice how the liquid has become more viscous, so as to adhere better to the ink on the page. The grand moment has come. I will drip a single droplet on the manuscript, and we will see whether the original text transpires." With one hand he stretched the manuscript as far as possible, aiming the pipet in his other hand betwixt his outstretched fingers. As he slowly pushed the stamper, a small droplet formed and detached itself. Then suddenly a flame burst out and Holmes shrieked, pulling back the hand from the manuscript where a fire was quickly eating through the old page. I grabbed an earthen jar with what looked like water and was about to pour it out on the fire, when with a superhuman effort Holmes blocked my action with his injured arm, grabbed a towel with his good hand and threw it on the flames. "Not the petrol," he said with clenched teeth, "unless you wish to blow a hole in the wall and wake up the whole neighborhood." Shocked I put the jar down, for the first time noticing the strong, repugnant smell emanating from it. My hands still shaking I helped him putting out the fire, when the door opened and Mrs. Hudson came in, harried and frightened. "Mr. Holmes, are you alright? Good Lord, look at your hand!" The little hairs on the back of his hand had been singed, and the palm of his hand was all red. It wouldn't take long before it started to blister. From the medicine case that Mrs. Hudson handed over to me, I took a balm cream and rubbed it on his palm before bandaging the hand and wrist. Holmes had regained his ascetic composure, and was looking at the burned remains of the manuscript. "Old, dry parchment like this is of course highly flammable. I might have foreseen that. Terribly sorry for the scare, Mrs. Hudson. We'll clean up the mess forthright." "You'll take it easy, Mr. Holmes," said she. "I will prepare a nice dinner for you and the Doctor, and then you will relax. No more experimenting to-night." "I can promise you that. Now, Watson, what do you make of this?" he asked, after the landlady left the room. "The University Library will not thank you for this. How do you think to repay them?" "Oh, they'd never let me enter their grounds if I'd have destroyed this invaluable manuscript. Luckily it's still here and in one piece," said he, producing said document from his coat pocket. "Good grief, I could have sworn it was the original." "An old conjurer's trick. While you were intently watching the distillation, your vision reduced by the leaden mask, I simply replaced the manuscript with a carefully prepared replica, containing one of my own monographs," he replied with a chuckle. Taking a closer look upon the untouched part of the parchment, instead of the Greek incantations of the prayer book, even if the letter type was quite similar, there stood in plain English: "On the noxious properties of flammable gases, by Sherlock Holmes". As I looked up at him, we both broke into an uncontrollable fit of laughter. After dinner we repaired to the study room for a smoke. The conversation inexorably drifted back to the events earlier that day at the Calhamer club. "You claimed that the maximum number of dislodgements, seven, can be achieved in the Fall of 1901. I still have a hard time believing that," said I. "Then get out the Diplomacy board and reconstruct the Fall position. You'll be so good as to avail yourself of pushing all the pieces, as I have been rather... handicapped," said Holmes, holding up his bandaged hand while drawing on his pipe with his other hand. "Well certainly." I took out the board and, using my notes, arranged the pieces as in the Fall 1901 situation of the solution given by my companion earlier that day.
"The first step is to determine what units were not involved in any dislodgements that season. These are the two Turkish armies, the single English army, and the French army occupying Burgundy. "We can immediately remove the English army from further consideration. She cannot be dislodged even if moving to Edinburgh or Yorkshire, and likewise she cannot attack or support an attack with the strength to dislodge unless through convoy. In the latter case the convoying fleet will not directly participate in the dislodgement and we're not much better off than if the fleet would attack herself." "Well then, the English army is out," said I. "That leaves the two Turkish armies and the French army in Burgundy. To my eyes the distance between France and Turkey is far too great as to arrange for a dislodgement of the French army." "And so it is," replied Holmes. "But we're not obliged to leave the other dislodgements as they are. Let us start with the two Turkish armies. Observe how they can be put to work in an attack on the Russian fleet opening to Armenia. This, by the way, is the only way in which both armies can participate. In all other instances at least one remains out of the picture, or else a neutral centre gets captured." "Ah, correct, I was thinking of opening to Bulgaria, but this would inevitably lead to the capture of a neutral centre, be it Rumania, Serbia or Bulgaria itself. Well then, Sevastopol moves to Armenia and Constantinople to Ankara. Ankara must then by necessity move out to the Black Sea, where it faces the Russian army in Sevastopol. But where is the third unit?" "There can only be one. There's no use in moving Warsaw closer, as that army cannot support an attack on its fellow army. That leaves the Austrian army in Budapest." "Budapest to Rumania, I see, placing it adjacent to Sevastopol and the Black Sea. Then the attack must be on Sevastopol, as Rumania is a neutral centre and the Black Sea a sea area, inaccessible to both armies." "Very well," said Holmes. "The picture should become clear now. You pull away one unit from somewhere else to complete this triplet, repeating the procedure on the triplet where it hailed from until one of the unemployed armies can be pulled in." "Right then. The Austrian army was pulled away from Galicia, leaving the Russian army in Silesia and the German army in Berlin in the cold. They started out from Warsaw and Munich respectively. Munich is next to Burgundy, where the French army is holding. Munich holds, Burgundy attacks, Silesia supports. We have found the seventh dislodgement."
Proudly I looked at my accomplishment. But a question was still lingering. "How then can you assert that this will not lead to a solution of the original puzzle?" "The answer should be self-evident from the simple fact that Sevastopol must be taken. Russia can only recapture it with an army in 1902, while the puzzle requires there to be a fleet. Even if the fleet would have survived 1901 to recapture Sevastopol in 1902, it would be the same fleet that started the game there, something explicitly forbidden by the rules of the puzzle." "But might there not be another arrangement that does not require the capture of Sevastopol? After all, you have so far demonstrated only one way to get to seven dislodgements." "No. We have already established the impotency of the English army. It follows then that all other 21 units must get involved, including both Turkish armies. These must attack Armenia, forcing in turn the Turkish fleet to participate in an attack involving Sevastopol of which there can only be one. The proof is conclusive." We remained silent for a while, smoking our pipes. As I was reflecting upon the "impotent" English army, my friend's mad dash to the telex came back to mind. That mysterious invitation to London, with excursions to Wales and the Channel islands, what had that been all about? Was it the Channel Islands themselves that bore some hint? What were their names? Gu... "Guernsey and Jersey," Holmes said, interrupting my thoughts. "And no, they are immaterial to understanding the invitation." Disconcerted I objected: "Was I speaking out loud? Or are you reading my mind? I do not remember uttering a single word." "The latter would come closer to the truth," said he, smiling. "To the astute observer there is no difficulty in following the thoughts of a person he has an acquaintance with. You had been ruffled by my calling the English army impotent, because as an Englishman you had subconsciously identified yourself with that army. I could see that from the way your brows became knitted and the corners of your mouth dropped. "Then your frowning became deeper, indicating that you attempted to analyze a previous topic. You stooped slightly forward to concentrate on the upper right corner of the board. Presumably you were attempting to disprove my claim that the Liverpool army could not be made part of a dislodgement by itself. Particularly having the army in Wales and the French fleet in the Channel must have drawn your attention, as it's the only situation where the army is adjacent to a foreign unit. You even considered placing the army in London, as your eyes flitted to the street map of London here above my desk. You dismissed then that thought as you realized that Liverpool and London are not adjacent, unconsciously shaking your head. "But then your expression became one of wonder as you connected London, Wales and the Channel to the message I wired at the club, reimagining the scene of my hurried delivery. Immediately your face darkened again as you tried to decipher the meaning. Your eyes went to the wall where there used to hang a map of England, which is unfortunately now in the custody of the University Library of Cambridge as a collateral for borrowing the palimpsest. You were actually casting your eyes to the bottom of where the map used to hang, indicating that you were searching for the Channel islands. Your mouth opened and your jaws stretched, as when forming a hard G-sound. That's when I came to your rescue." I was again struck with awe by the apparent facility in which he had deduced my hidden thoughts. But I could not deny a certain discomfort with being exposed like this. "Well, since it's hard to keep any secrets from you, at least you can do me the favor of answering my unspoken question." "Oh, but there's no great mystery to it. It had simply occurred to me that there is another way to reach 15 dislodgements." "But in that case the solution is not unique, and the problem unanswerable." "Not true. This second solution requires more than one retreat, while the Sultan mentioned only a single retreat. In order to explain, it would do well to return the board to the start of Fall of 1901. "Good. Now, we make two changes. London is sent to Wales and Liverpool holds. In the Fall we dislodge the French fleet in the Channel with the fleet from Wales, supported by the second fleet in the North Sea. Liverpool still holds, while the other moves remain the same. Now, instead of disbanding the French fleet, let it retreat to London."
Reflecting upon this, I remarked: "In other words, the invitation to London is actually a retreat to London. Losing London means England is forced to disband a unit. Its army, I presume. But how do you plan to dispose of the French fleet now? Attacking it with the two English fleets will prevent the Channel fleet from reaching Edinburgh, as we have discussed before. Could it be that you overlooked this?" "My dear Watson, I will not claim that I'm infallible, but not on this occasion. Just as England lost a centre, France gained one, allowing us to build a second French fleet in Brest." I was still not certain where this was leading to, but nonetheless took a second fleet out of the box and placed it in Brest, while removing the English army.
"Observe that France now has 4 units. All that is required is for England to recapture London to put France at a supply deficit." "A disband in Winter 1902! That indeed makes a dislodgement superfluous. As England sends its Channel fleet over North Sea to Edinburgh, it retakes London with its other fleet whence the French fleet moves out, to Wales I would think?" "Except that the objective is to make as many dislodgements as possible," said he, pointing the mouth piece of his pipe first at me, then at the board. "In Spring of 1902, let North Sea attack London with support from the Channel to dislodge the French fleet for the second time. This time let it retreat to Wales. In Fall let it dislodge the English fleet in the Channel with support from Brest. England disbands its fleet and rebuilds it in Edinburgh, returning to its starting position." "Brilliant! So London, Wales and the Channel are the locations of the first French fleet. Two dislodgements in 1902, where originally there was only the one attack on the English army. Could it be that this solution has 16 dislodgements then, one more than the original? Is this than not the true solution?" "No. As I mentioned before, the Sultan's riddle explicitly mentioned only one retreat, while here we have two more, therefore it cannot lead to the solution that the Sultan had in mind. Furthermore I need to disappoint you, but even this approach leads to 15 dislodgements at the most. The reason is that for France to be able to disband its Channel fleet, it must have all its other units survive and every home centre occupied by one. Thus sending Burgundy to Munich in the Spring of 1902 is out of the question, for that unit, if dislodged, cannot retreat to Marseilles, and neither can it disband. Therefore, depending on where the Austrian army in Silesia retreats to, one dislodgement, either Munich or Warsaw, will not transpire, and the total number will remain at 15."
I was not yet convinced. "Is there then no way to go beyond 15 if the number of retreats is unbounded?" Holmes looked despondently at his bandaged hand. "That's the burning question. But I need to uphold my promise to Mrs. Hudson: no more experiments to-night. Let us rest the case." There was no arguing that. I too felt my energy sapped by the events of the day. We smoked our pipes in silence and before long I bid him farewell.
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