This article offers a solution to the "A Challenge from Devonshire" case presented in the F2008R Zine. Readers acquainted with the case may observe a few recent changes to the note in that article. These were made to ensure, to the best of our knowledge, a unique outcome in line with what the authors designed. The reason behind each of them will be explained more thoroughly in an upcoming article. Notwithstanding, anyone able to solve the original riddle, even if the end position differs, deserves full credit for the feat. You may still send your solutions, or remarks, to the Pouch.
Deducing the final season
Holmes, now assured of an attentive audience, took place in the chair normally reserved to the Game Master before finally coming round to indulge us with his observations. "Let us start with the easier part. Gentlemen, how long will it likely take to reach the final position at the earliest occasion?"
"What rot!" said the red-headed man snidely. "I'm more adept at increasing my unit tally than at reducing it. I leave that to my opponents."
"Be a sport, good man," Holmes replied with a chuckle. "It's not a tricky question. I'll give you a hint: It could be done in one game year!"
"What? I say, you're mocking me. Show us!" the red-head exclaimed as his cheeks turned close to the color of his hair.
"…if one were allowed to arrange the starting position at will."
"Which is not the case, but show us anyway," I said as I watched the rattled rosy-cheeked man attempt to regain his composure.
"Elementary arithmetic, my dear Watson. There are twenty-two units at the start of the game. What means do we have at our disposal to remove units and how many units are involved in such endeavors?"
"There's dislodgement," I offered, "which requires two units for every dislodged unit, but it must be followed by retreating off the board…"
"Or bouncing during retreat," a helpful voice added.
"And capturing centers from other Powers, which only requires one unit for every unit removed," the red-headed man, now a bit calmer, threw in.
"…provided the attacked party did not offset his losses elsewhere or lost units during the year, or had less units than centers to start with," I pointed out.
"Moreover, dislodgement can be done in every Spring and Fall season, whereas capturing is only effective in Fall, with removal during Winter adjustments."
"Correct," said Holmes. "So, starting with 22 units set up in an ideal arrangement, after the first Spring season at most 7 may be dislodged — a ratio of 1:3, rounding down — so 15 remain. In Fall another 5 can be dislodged — the very same ratio — leaving 10 units, of which 5 may at most be removed during Winter, a 1:2 ratio, less than the 6 given in the riddle."
Holmes, for the sake of the argument, oversimplifies. What do you think the actual minimum is: 5, 6 or 7? Can you demonstrate it on the Diplomacy board? Click here for a solution.
"All jolly and well. But we know that the starting position is fixed and that no unit can be dislodged in the first season," the man in the Eton blazer remarked.
"I'm pleased to see, Sir, that you pay attention to the board," Holmes said with a twinkle in his eyes. "For indeed, one will never encounter a S1901R phase in a genuine game of Diplomacy, as no unit, not even Venice or Trieste, is adjacent to two enemy units at the start."
"Holmes, are you suggesting that two full game years will suffice?" I inquired, putting two and two together in my mind.
A man with a dark skin and a foreign appearance suddenly spoke up: "Can it not end a season earlier, say in Fall 1902, instead of Winter 1902?"
Holmes responded calmly: "If so, it would be quite a miracle. To understand that, let us work backwards. 6 units after the Fall 1902 Retreats means at most nine units after the Spring 1902 Retreats (factor 3:2), thus 13 units after Winter 1901 (the same factor, rounding down). This means that in the first year at least nine units should be eliminated.
"Take my word, you will find it excruciatingly difficult to eliminate that many in the first year. In the rare case you might succeed, it's very hard to imagine that the remaining 13 will be in an ideal spot to whittle down to six in two seasons, as the Fall 1902 Retreat final requires, and at the same time satisfy all other constraints imposed by the riddle. On the other hand, fellows, with an extra Winter season we acquire a lot more flexibility.
We already know that a fully arranged board can be brought down to six units in a full game year. Let the first game year set the stage, and every unit removed in it can only ease the burden of the chore left in the second year. Therefore we should aim for two full game years, no more, no less."
The dark skinned man looked unconvinced, but the others were willing to concede, convinced that the Great Detective was simply saving them from a lengthy and quite boring analysis, curried with more "elementary" arithmetic — that would inevitably have a dampening impact on their further evening plans.
A challenge on the side: Holmes didn't say that eliminating 9 units in the first year is impossible. In fact, he can prove that it is feasible, but not in a way that will lead to a solution of the riddle. Can you do as well, or even best his result? The best answer will be included in the next Zine.
Events in the South
Holmes, for his part, seemed not to mind as he glanced once more at the note before laying it down next to the board. "Now, chaps, to solve the riddle, we get one extremely useful hint: At the end there will be only armies left — two armies each of three different colors. All fleets must disappear, and four of the seven Powers will be left with no units. Who do you suspect will be among those 4?"
"Well, England, obviously, as it starts with only one army, " the man in the Eton blazer said, with a proud smile.
"Not necessarily correct: Great Britain could build an army."
"What! Builds are allowed?" the man replied in shock as he took off his blazer and sat down at the table across Holmes.
"There's no statement to the contrary. But I concur that it's unlikely to be the case here. So, England is one of the four. Which other Powers?"
"All other Powers start with 2 armies. I must confess to be clueless, " the man answered and pulled back from the table, sheepishly looking down at his lap.
Holmes was clearly enjoying himself, as he glanced at the bespectacled man who was taking notes. The man had now taken off his glasses to better read the letter from Devonshire. "How would you go about eliminating a Power? The most effective method is by robbing it of all its centers, no?"
"Certainly so. Oh, wait, the letter mentions Army Marseilles… France?" the note-taker observed, putting on his glasses again.
"Indeed. An army in one of the French home centers is a telltale sign that France is one of the targets."
"But Holmes, couldn't it be merely there to remove the fleet?" I suggested.
"It could, but then you are left with two French armies that are not allowed to conquer a single center. That amounts to one third of your remaining stock not participating in conquering centers in the final season. A heavy burden, even if we assume that A Tyr is French."
Holmes was clearly thinking far ahead of us, as none of us had yet considered where we'd want those armies to be at the end of the game, except in the places mentioned in the letter.
His following question took most of us by surprise: "What about the East?"
"We know very little about the East," the dark-skinned man said, as if he had been waiting for this. "All the hints we have are regarding the Western theater."
"What does this tell you about Turkey?" Holmes continued.
"Nothing, and thus, everything!" I exclaimed. "Holmes, it's the same as the missing fleets. If all action is concentrated elsewhere, the Turks were either extremely active, or expeditiously wiped out."
"The latter is more likely, given the distances involved and the short timeframe. Have you heard of a movement called the Young Turks?" asked Holmes.
Indeed I had: "I have heard rumors they're planning a revolution, and are secretly mustering for support among the other Great Powers. Some would go as far as to invite foreign armies on their soil in order to topple the current government." The dark man was gazing at me, with what seemed like an air of contempt.
"Rumors, Watson, don't pay heed to them," Holmes reassured us. "I'm sure the majority are bona fide nationalists, not at all prepared to sell out their country. But if it were the case, the following will demonstrate how easy it is to eliminate the Ottoman stronghold with the assistance of their own people, at least on the Diplomacy board." It did little to appease the foreigner, but the tall man to his right whispered to him briefly, and he stepped back a bit.
"Let's see what units can move into Turkish home centers in the first year," Holmes continued.
The tall man spoke up now: "Fleet Sevastopol of course, and Moscow if convoyed. Given that Turkey cooperates, Fleet Ankara moving to Black Sea can do the convoy to Constantinople, while Sevastopol moves through Armenia to take Ankara. That's two centers taken."
"Not bad," Holmes congratulated him. "But it's better to have another color in the mix." He started to move a few pieces on the board. "Let us use the Austrian army Budapest instead of Russian Army Moscow, and send it to Rumania for the convoy. Constantinople evacuates to Smyrna, Smyrna to Armenia, which is the unit we'll keep around after Winter. In the second year Austrian Army Constantinople dislodges the Russian fleet in Ankara with the help of the remaining Turkish unit, then moves on to Smyrna to eliminate his friend."
"Holmes, that’s simply amazing!" I cried. "You've got rid of 4 units, including the Russian Black Sea fleet with a single army, more or less!"
While the others nodded and talked softly among themselves about the possibilities, the man in the Eton blazer remarked: "We still have to figure out the identity of the fourth eliminated Power."
"But we're getting pretty close, " the red-headed man chimed in. "And we already know the identity of one survivor: Austria."
"Furthermore," the tall man added, "if Russia is going to be eliminated, it will not be through loss of all her centers, because she just gained Ankara."
Turkey, Fall 1901
Holmes turned his attention to another part of the board: "Speaking of surprises, does anyone remember what happened last year during the Venetian Carnival?"
A dashing young man raised his voice: "As if I could forget! It had been my wife's dream to visit the Carnival, and so for our anniversary I surprised her with tickets for a long-overdue holiday. But what a holiday it was. No sooner had we set foot on the quay, than we heard a loud explosion — and the largest vessel moored there, the 'Pride of Naples', took fire and began to sink. You can imagine the commotion. A special police squad from Rome was dispatched, who, after a long and classified investigation, confiscated an anonymous boat and its crew. The press wasn't informed of the crew’s nationality. But what does this have to do with our riddle?"
"I had for a long time held a suspicion that Moriarty had been involved, and here we get proof that he knew more," Holmes informed us, grimly.
"You see, there's quite a simple way of getting rid of both the Austrian and Italian fleets. First Fleet Trieste moves to Venice in Fall 1901, with Venice moving out. Italy, with only two centers left, removes Fleet Naples. In Spring 1902 Army Rome dislodges the Austrian fleet, supported by the other Italian army, or some third party."
"So the assailants were Austrian?" the handsome man asked.
"Or so Moriarty wants us to believe," Holmes answered.
"Wait," I interjected, "if one Italian army is in Venice in Spring 1902, and the other army in Piedmont, then these can move to Tyrolia and Marseilles in the Fall. We have solved the riddle!"
"Not so fast," Holmes said reproachfully. "We have simply established a plausible identity for the armies mentioned in the note. There's still the matter of determining the position and color of three other armies, and the owner of each supply center."
Italy, Spring 1902
Brilliance up North
Another man, sporting a huge moustache, was clearly getting impatient, and demanded, "So will you tell us now who the fourth eliminated power is? Is it Germany? Is it Russia?"
"You already know the answer," Holmes said, smiling. "If not, you'd do well to study the English and French position first. Assuming that France will lose all her centers, how can it be accomplished?"
The man with the moustache immediately answered: "Easy! German Army Munich can move to Paris in 1901, and to Brest in 1902. Together with the Italian Army Marseilles, that spells the end for France."
"Right-o," said Holmes. "But is there any other way to accomplish the same?"
The man in the chair moved a few pieces and stroked his chin, saying, "In theory Army Liverpool could be convoyed to Brest and then move to Paris, but we know that England needs to be eliminated, so that's not an option."
"Perhaps, perhaps,” Holmes said thoughtfully. “But England needs only to be eliminated at the end of 1902. She can take a center in 1901 if her units get dislodged the following year. And given that Paris is adjacent to Brest, the army could move in there first, then be dislodged by an army from a different power — see?"
"Such as Austria, " the red-headed man exclaimed. "Holmes, this is excellent! Army Vienna could move to Munich in 1901, then on to Paris in 1902 and dislodge our friend from Liverpool with the help of a French army."
The man with the moustache shook his head in disbelief, asking: "Did you say Munich in 1901? The last eliminated power is Germany?"
"One could expect as much," Holmes answered. "We know that Russia is gaining centers, and that England is too remote to lose all her home centers: convoys are costly, and its nearest opponent, France, is not allowed to take centers, if we follow our own logic. Eliminating a power by taking centers is more efficient than by dislodging its units, as the units of such powers can play a supportive role right up to the Winter turn. Case in point: Turkey."
France, Fall 1902
"Yes, but all supply centers listed in the riddle are close to Germany. How will you conquer these if neither France nor Germany can take them?" the man with the moustache protested.
Holmes smiled as he reflected upon Moriarty’s twisted brilliance, saying, "It is here that we see the master mind laying his snares to confuse a lesser mind. Yet the path is clear if careful attention is paid to both the problem description and the problem space."
He pointed at the note, then gestured toward the board. "Three neutrals must be taken in the North, in addition to Brest. England can only capture three of these in 1901, Russia one (Norway). Yet if we look closer, we can see that England cannot at the same time take Holland, Belgium and Brest. For, to take Holland and Belgium, it must move its fleets to the Channel and North Sea in Spring. Fleet English Channel can either convoy Army Wales to Brest or move to Belgium, but not do both. So although, with the help of the French fleet, England could take three centers (one being Norway), not all four can be occupied in 1901 by England and Russia combined. This does not need to be a problem, as we have singled out Russia as one of the surviving powers, so Russia could take the fourth center in 1902."
"Which center should remain open then?" I asked. "The convoy to Brest means the choice is between Holland and Belgium. Both are adjacent to the North Sea, through which the English fleet must pass."
"Elementary, my dear Watson," Holmes replied. "Which one will the Russian army take in the second year? England simply has to take the other one."
"Quite so," said the tall man thoughtfully. "Given that Austria is moving to Munich, Warsaw can only go through Berlin in 1901 and reach Holland in 1902. Moscow could follow, but would only reach Kiel."
"Which isn't so bad," Holmes said. "Bear in mind that those same armies need to also capture two German home centers. Starting with Berlin in 1901 and following up with Kiel and Holland or Belgium in 1902 is just what we need. But there are other routes."
The tall man thought for a moment, then said: "Right, we could send Moscow north to Norway, then move — no — convoy to Belgium or Holland in 1902! Speaking of convoys, why not convoy through the Baltic Sea to Kiel in 1901? That would finish off the German immediately. We'd only have to worry about one more center!"
"Steady as she goes," Holmes cautioned. "There's one more piece to the puzzle: how to get rid of all the Northern fleets. France and Germany will remove theirs when their home centers are captured. What about the English and Russian fleets? How early can they be dislodged?"
"None, obviously, in Spring 1901," remarked the man with the moustache. "In Fall 1901? Let me see… Wait! There's the Sealion: It requires France successfully moving to the Channel, and the German fleet to move to one of the spaces bordering the North Sea. Then the English fleet in that sea, whichever it is, may be dislodged."
Holmes dismissed this, saying: "This is not a very attractive set of options, sir, as this would both prevent the convoy to Brest and the taking of either Belgium or Holland. No, the English fleets for better or worse will both survive the first year. What about the Russian fleet on the south coast of St. Petersburg?"
The tall man interjected: "Well, this may be almost too obvious, but if Germany moves its units to Baltic Sea and Prussia, and Russia its fleet to Livonia, the German units can dislodge the latter."
"Excellent use of disposable units, getting rid of one major obstacle. Go on," Holmes said, with an encouraging smile.
"I see," the tall man continued. "If the Baltic fleet is thus occupied, no convoy will occur. So Moscow either trails Warsaw, or it circles through Norway, then convoys to cut in front of the other army."
Baltic Sea, Spring 1901
"But isn't Norway where Edinburgh is headed?" I wondered out loud.
Holmes shook his head. "That would be too slow. To accomplish the feat in the least number of moves, as the note urges us to do, it needs to be in the North Sea at the start of the second year. Have you kept track of the number of French and German units that remain after the first year?"
"Well, France only loses Brest, so may keep two units. The Germans only retain Kiel, so are entitled to only one," the bespectacled man counted, while checking his notes.
"Having a sufficient number of these units can mean the difference between success and failure, my dear friend. Three will do. What task did we reserve for the French army?" Holmes asked professorially.
The bespectacled man looked up from his notes: "That would be supporting the Austrian army into Paris."
"Which it can perfectly do from Picardy," Holmes noted. "That means that in Spring either that army or the fleet in the Channel can support the convoy to Belgium to dislodge the first English fleet."
"A Spring convoy?!" I nearly shouted in surprise. "It sounds like you want to use the second fleet as a stepping stone for the Russian army in Norway. But, my dear Holmes, this will leave the fleet in the water! How on earth will you get rid of it in the last season? Where are your two… fleets?…“
And then I had a flash of recognition. “By Jove, you're planning to send the Baltic Sea fleet through Denmark to blow Fleet North Sea out of the water with the help of the French fleet in the Channel! Brilliant!"
"To be swift, we must act boldly, my dear Watson,” Holmes replied. “To finish our puzzle, Russian army Belgium advances to Holland, the units from the eliminated powers are removed, and the final position is revealed."
And with that Holmes, spent from delivering his intense lesson, reclined in his chair with an expression on his face, which did not reflect idle satisfaction for his own accomplishment — but rather honest admiration for the ingenuity of his opponent.
North Sea, Spring 1902
Click here for the complete solution.
As everyone congratulated Holmes on another case well-solved, the red- headed man asked: "So, where will we take it from here? With only six armies left, scattered across the board, there seems not to be a lot we can do until the next build phase."
"I don't think the Devonshire club will object if we add two seasons to the game record," Holmes said with a smile.
"What with the hunts and all," another man exclaimed, grinning.
Holmes continued, "Well, then, let us remove one more unit, complete the Russian conquest of Germany and furthermore ensure that during Winter as few fleets can be built as possible."
"A tall order," the red-headed man said.
"Not necessarily," the tall man said, his eyes studying the board. "Russia must move an army to Munich. Let that be Kiel, and let's move Holland to Belgium or Ruhr, and the Austrian army in Paris back to Burgundy. In Fall Munich assists the second Russian army in dislodging the Austrian, who retreats off the board."
"Then Austria will counter by taking Russia's Black Sea port, Sevastopol, with her army in Smyrna," the red-headed man said defiantly.
"But she will lose her own port when Italy moves Tyrolia to Trieste. At the same time the army in Marseilles can retake Venice. Austria is going down hard," the handsome man beamed.
"And so it should be. She deserves a good spanking after what she did to the Italian national pride."
"Sorry to interrupt, but I did say as few fleets as possible," Holmes said pointedly. He put the pieces back to their W1902A position and then proceeded to move them in such a deft way that left us once again perplexed.
"Well, whatever happens to the rest of the board, Britain will rise again from the ashes," the man in the chair said, while standing up and donning his blazer. "Beaten back, but never buried."
"God save the Queen!" the others saluted.
True to form, Holmes has prepared a trap of his own for Moriarty in this contest of wits. Can you find a way to restrict the number of fleet builds to less than six, while still satisfying the other two conditions put forward by Holmes? You can send your solution to the Pouch.
-- Dr. John H. Watson
If you wish to e-mail feedback on this article to the author, and clicking on the envelope above does not work for you, feel free to use the "Dear DP..." mail interface.