Sherlock Holmes,
Consulting Diplomat

by Mario Huys,
Master Ænigmatist


Solution to "The Costly Case of the Last Man Standing, Part 2"

The room was empty now except for the two of us, but there was still a nice fire burning in the hearth. Sherlock Holmes went to the bar and poured us a drink. I gladly accepted mine. We took a sip and relaxed in our chairs.

"It was not my intention to be cruel to you," he said. "You're obviously in no state now to work out this puzzle."

"It has been quite an eventful evening," I admitted, happy to extract myself from any further intellectual exercises. "But you must tell me how you were able to instantly know how the game had played out, with Sir Malcolm collapsing on the floor as an extra distraction. Had Mr. Waltman from the Diplomacy in Kent magazine tipped you off with another challenge, as in the case of the first LMS game?"

"He did not. I only heard of a second game this morning, when Sir Malcolm mentioned it on his way out, unaware of any of its conditions except for the Baron's boast that it would be more spectacular than the first one."

Holmes took a sip of his drink, taxing me with a glimmer in his eyes. I was as ever his faithful audience, eager to hear another wondrous tale of how he had found clues where there were none, solving problems that had not even occurred.

"As I told you, I had the whole afternoon off. Having made myself some kind of an expert on Last Man Standing puzzles with my treatise on the subject for the Diplomacy in Kent magazine, I considered it a suitable challenge to predict the kind of game that the Baron had prepared."

He was referring to the at that time still unpublished series of articles for Douglas Waltman's rival magazine to the Zine, which still drew some of my ire. In these he demonstrated all the capitals army Liverpool could reach as the Last Man Standing under the same conditions as in the Baron's first game.

"Remember the conditions he had imposed on his Liverpool to Berlin game. Finish in four years with all powers still possessing at least one unit after two years and no neutral centers taken. If there's one condition to change, which one would it be?"

It was more of a rhetorical question, at least to him. "Try what may, it can't be done in three years, this much I knew. Reducing the number of powers early is hardly spectacular and risks disengaging prematurely part of the public that had been betting on those powers. But neutral centers are fair game. None taken restricts the number of places a unit can be on after the Fall turn. Take that condition away, better still, put it on its head, and the possibilities become quasi limitless."

"Well then, even you are not going to solve a problem with limitless options," I remarked.

"Indeed not. Unless you take the human factor into account. With all the information that I had, it only takes a few judicious assumptions to reduce the problem to a manageable level. Baron Hervé had his solution to the no-neutrals problem as a starting point. All he had to do -all I had to do- was to make small, incremental variations that gradually captured more and more neutral centers, while keeping the same basic game flow."

"But how could you be sure that this approach would lead to such a large capture of neutral centers?"

"There were a number of indications that this would be the case. First off, in the original solution there were just three units going into the final year. As you must be aware by now, the maximum number of units going into the final year is four. Allowing one extra unit in the final year translates in more extra units in the previous year and thus more positions to move them to. Furthermore, remember that there were two powers that got completely eliminated, Germany and Russia."

"Oh yes, the sniper countries."

"As you please. The more snipers there are in the early stages, the easier it is to pick off units that moved too far out to reach the destination. When trying to capture neutral centers, which are distributed fairly evenly around the board, this is an important factor. And finally, with neutral centers allowed to be captured, you can aim at landing all three non-sniper units -which we called raiders- on a supply center at the end of the third year."

"I see, Kiel is connected to Holland and Denmark, and then to Belgium and the rest of Scandinavia. But what advantage can be gotten from that?"

"If all those centers belonged to the sniper powers, capturing them allows to disband a maximum number of snipers. Or, in other words, allows for a maximum number of them to survive into the third year."

"Three centers captured in the Fall of 1903 means there can be four sniper units at the start of 1903, including the one that will still be there in 1904."

My curiosity piqued, I got up and stood next to the giant demonstration board. Without removing the country flag markers, I took the pieces one by one out of the box and set up the initial position for 1901. They were cast in iron and the size of a fist, richly decorated and quite realistic, but also heavy. The pieces were pushed around using a kind of roulette rake. I took it up and proceeded to execute the moves for the no-neutrals solution, which was still fresh on my mind.

"The English fleet moving to St. Petersburg could move through Norway instead of the Barents Sea in the Fall of 1901. That would net Norway for England. With Denmark blue I assume that you're moving the second fleet there."

"Ah, Watson, now you're reasoning from the end result. That won't do. If you really wish to understand the singular progression of the mind, you should put yourself in the same situation." And with that he cleared all flags from the board, much to my dismay. He motioned me to sit down and took the rake in his hand.

"Norway is a giveaway. As is actually Belgium, if you use fleet Brest to convoy the English army, allowing fleet London to move to Belgium. The logical next step is to transpose the events in France to the Lowlands, letting Germany take Belgium instead of Paris, England take Holland instead of Brest and convoying to Picardy."

"But if France doesn't lose any centers, it prevents the French fleet from disbanding."

Holmes shrugged. "Once you start taking extra centers, disbanding units in Winter will be a lesser used tactic, especially in the first year. The trick is to create an extra opportunity to dislodge a unit. One such occasion is Spring 1902, when the three armies in France were simply dancing around each other. In the present variation the armies and fleets are clustered closer together and on land. We can have the French army in Ruhr supporting the German army to Holland to take out the English fleet, then being dislodged in turn when the English army, now in Burgundy, supports the German army in Ruhr, while the French fleet takes Belgium."

"And if the German army then attacks the French fleet in Spring 1903 and moves out in Fall, we have the same endgame as in the original. Beautiful. But still only three neutrals."

Click here to open or close the final map and here for the complete history of this solution.

Holmes smiled. He was clearly enjoying this. "You tell me if I'm going too slow. We're coming to Denmark now, which you were going to capture with the fleet from London. Try now to make this work." And with that he handed the rake back to me.

Dr. Watson is called to the table again. A cue for you to step in his shoes. And if one is not enough, try Sweden as well. How far do you get?

...and when you're ready to continue with Watson's tale, click here....

— Dr John H. Watson
via Mario Huys (woelpad@gmail.com)

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