My friend Sherlock Holmes had just announced to the Foreign Secretary Lord Reginald Fortescue and me that he had determined how to resolve the clever riddle posed by the Diplomacy-playing Sultan of Suwat. I have earlier described the details of this conundrum under the heading Begone And Back, this phrase having appeared in the cryptic instructions given by the Sultan.
"Certainly you cannot be serious, Holmes!" I repeated. "How can we possibly play a game of Diplomacy forward from a position without any idea what plans any of the players may have?"
Holmes smiled. "Obviously, Watson, there must be a way, since the Sultan's instructions that we do so are quite clear." (In fact, they were not very clear to me, but Holmes had explained the meaning of the Sultan's written message, or at least part of it.)
Lord Fortescue took the lead now. "Holmes, perhaps you had better walk us through your logic. You have explained the meaning of the third part of the Sultan's message, but I still see no way to determine what orders each power will issue in each phase going forward."
"Perhaps I should, then, milord," Holmes said, and with this, he pointed again at the Sultan's message which had accompanied the Spring and Fall 1901 Movement phase orders for this strange game.
"As you know, gentlemen, we have already discussed the third portion of the message. It is instructing us to play the game forward from the position given us, determining the final two neutral supply centres that are captured in the course of the game. Once we have done so, it is clear that we are to send an emissary of His Majesty's government on a round-trip voyage from the first of these two locations to be cautured, to the other, where the Sultan will be waiting to conclude the lease agreement."
I was anxious to get to the heart of the matter. "Yes, yes, Holmes; we understand this, but it is the how that seems to be a completely impossible mystery to solve!"
"Yes, indeed, Holmes," added Lord Reginald. "What we have is the position and centre counts for the seven players at the end of the first game-year, but how are we to know what each player will do from here? Specifically, the first order of business would seem to be the determination of orders to be issued in the Winter 1901 adjustment phase. How can this be done?"
"Elementary, fellows. Take a look at the second portion of the Sultan's message, which consists of two separate parts. The first of these, reading, 'Compulsory: build aquatic' tells us what to do for each player who has earned builds in the adjustment phase. The second part, reading, 'As board centres diminish, eliminate (firstly: ground)' is similarly informative if a player is in the situation where he must remove one or more units."
I took a cautious step forward and pointed at the message. "'Build aquatic' seems straightforward enough, Holmes. Am I right to conclude that all builds must be fleets?"
"Precisely, Watson! Well done."
"Still, Holmes," I continued, "I do not see how this gives us all the necessary information we will need. Take England's situation, for example. That player is eligible to build one unit. Although we know it must be a fleet, all three of his build centres -- Edinburgh, Liverpool, and London -- are vacant. How do we know where England will choose to build the fleet?"
"Ah, here, Watson, we must take note of the curious pattern of words that the Sultan chose when writing his message."
Lord Reginald spoke up here. "By that, Holmes, do you mean the fact that the initial letters of the words in the Sultan's message seem to be arranged in some sort of alphabetical order?"
"Precisely, milord! This, in fact, is the key to the entire mystery!"
I looked at the message, and realised what I had somehow missed. The initial letters of the words were indeed in alphabetical order, sometimes going forward in the alphabet, sometimes reversing direction and going backwards. Before I could ask my next question, Holmes continued his explanation.
"For the part of the message describing builds, the words, as you can see, are in reverse alphabetical order: 'Compulsory: build aquatic.' C, B, A, gentlemen. Telling us that builds are to be taken in the available build centre last in alphabetical order. In the case of England, then, his Winter 1901 Adjustment phase order is to build a fleet..."
"...in London!" I interrupted. "Of the three build centres, London is the third in alphabetical order."
"It is indeed, Watson, but I am afraid that is not where England must build his fleet."
Lord Reginald and I were both quite confused by this. "But Holmes! Didn't you just say...?"
"Ah, perhaps we should have discussed the moves that were given to us first, and what those can tell us. Shall we do so now?" Holmes asked.
"I suppose so," said a flustered Foreign Secretary. "However, can we not finish with the second part of the message, if you would be so kind as to tell us about the instructions for unit removal?"
"Certainly, milord. The instruction for removal is quite similar to the instructions for builds. It reads, 'As board centres diminish, eliminate (firstly: ground).' We can conclude from this that when a power must remove units, he should remove armies (if he has any) in preference to fleets. Notice the ordering of the words, in strict alphabetical order: A, B, C, D, E, F, G. This indicates that the first unit to be removed would be whichever army is located at the space which is earliest alphabetically. If a power must remove more than one unit, he simply applies this rule twice, moving to the removal of fleets (again, in alphabetical order by location) only when his supply of armies is exhausted."
I saw his logic, and I hesitantly offered the next conclusion. "I would think, then, Holmes, that this means that the French player, who must remove a unit at the end of 1901, would remove the army in Picardy, since his other army is in Piedmont, and 'Picardy' is earlier alphabetically than is 'Piedmont'. I say that I would think this, Holmes, but for the fact that you indicated that England will not build in London, despite it being the centre I had thought was indicated by the Sultan's build instructions."
"You are correct, Watson, that France will remove Picardy, for precisely the reason you gave. The situation as regards the English build centres is a bit different. Let us explore what the movements of the pieces during the first game-year can tell us.
"Consider, gentlemen, that we have now addressed the reasoning to be used for both build and removal orders; what remains are the very important movement phase instructions. Note, if you will, that the first part of the Sultan's message (that given before the build and removal instructions) and the third part (that given after the adjustment phase instructions) are both given to us in blue. Note also, that not only do these two parts of the message have the same occasional reversal in their alphabetical ordering of words, but that if the adjustment instructions did not intervene, both sets of blue text would join seamlessly without any interruption in the pattern."
"Yes, I see what you mean, Holmes!" said Lord Reginald. "The blue text must be the movement phase instructions, and the fact that the pattern is not interrupted by the adjustment phase instructions must mean that the units have some sort of 'memory' from year to year?"
"Very well said, Lord Reginald. Not only from year to year, but turn to turn. The curious alphabetical pattern of the words in the movement phase instructions, combined with what we can see from the actual moves that have been given to us, will prove to be all we need."
I was quite lost at this point. "Holmes," I said, "you and Lord Fortescue speak of a 'pattern'. I see no real pattern in the blue text! I can see that each word begins with a letter that is either forward or backward in the alphabet from the initial letter of the previous word, but I see no pattern in the various changes of direction. Am I mistaken?"
"You are not, Watson," said Holmes (which made me feel a bit of pride mingle with my continuing confusion). "There is no real 'pattern' to the up-the-alphabet, down-the-alphabet reversals that we see in the text. To learn more, we must go to the 1901 moves themselves, which the Sultan has supplied to us." Holmes spread them out on the table.
"Take a look, gentlemen, at the orders issued by each unit in the Spring 1901 phase, keeping in mind that the alphabetical order of the various spaces is key."
For a couple of minutes, the Foreign Secretary and I looked at the maps while Holmes puffed on his pipe. Lord Reginald beat me to the punch, and suddenly erupted, "I see it, Holmes! Each and every one of the units was ordered to the space which, among all possible spaces to which the unit could move, was the one that comes last alphabetically before the space on which it stands! Marseilles, which could move to Piedmont, Spain, Gascony, or Burgundy, was ordered to Gascony, because, of these four, Gascony is the space that comes just before Marseilles alphabetically!"
"Quite right, milord! That is exactly what was done, and why. If you will notice, the Sultan even hinted at this by beginning his movement phase instructions (those given in blue) with a movement up the alphabet, as it were, from the 'B' of his first word, 'begone', to the 'A' of his second word, 'and'."
I saw problems, though. "Wait a tick, fellows. What about the fleet in Ankara? It was ordered to Constantinople. Surely 'Constantinople' is later in the alphabet, not earlier, than is 'Ankara'!"
Holmes smiled. "Would you like to take this one, Lord Reginald?"
"My pleasure, Holmes." The Foreign Secretary beamed, happy in the confidence of my friend and more than willing to prove that it was merited. "Take an inventory, Watson, of the spaces to which the Ankara fleet could have been ordered. In alphabetical order, its choices were Armenia, the Black Sea, and Constantinople."
I interrupted. "Precisely my point, milord. None of these spaces precedes 'Ankara' in alphabetical order."
"Yet we know that the unit did move to Constantinople, Doctor. Which tells us that when determining alphabetical order, we must continue beyond one end of the alphabet to the other. Since no space preceded 'Ankara' in the alphabet, we continue to look beyond 'A', moving up again from 'Z'. The alphabet simply repeats, so that all units always have a movement order to attempt."
"Well said, Lord Reginald!" offered Holmes. "In fact, the Sultan told us in his message that this would happen occasionally. As you can see, more than once in the blue text his words slip from 'A' to 'Z' and back."
This all made sense to me, and when I looked at the board with this in mind, I saw that in the Spring move, each of the units had indeed done exactly what the Foreign Secretary outlined. "Excellent!" I exclaimed. "If each of the units simply moves up the alphabet from space to space and turn to turn, and with the instructions we have regarding the builds and removals that the powers should execute each Winter as needed, we can indeed play the game forward! The puzzle is solved!"
"Not quite so fast, Doctor. As I recall, we weren't clear yet on England's build for some reason," said Lord Reginald. "Mr. Holmes seems to have divined some other detail that we have not."
I was a bit deflated, having thought we could proceed to simply moving the pieces and solving the mystery. "Quite right. Holmes, what are we missing?" I asked.
"Well, firstly, Watson, the units do not simply move up the alphabet from turn to turn. As you recall, the words in the movement phase instructions we were given (those in blue) change direction, sometimes moving 'up', and sometimes moving 'down' the alphabet. So we know that sometimes, units will do this as well. We have just looked at the Spring moves and seen that every unit moved 'up' the alphabet -- that is, in the direction from 'Z' towards 'A'. Shall we take a look at the behaviour of the units in the Fall?"
We did just that, the Foreign Secretary and I again looking at the moves while Holmes pulled contentedly from his pipe.
Once again, Lord Fortescue was first to speak (although in my own defence, I believe that I was as ready as he to announce a finding). "Holmes! You are right! In the Fall, some of the units are continuing to move 'up' the alphabet towards 'A' but others are moving 'down', towards 'Z'!"
"Indeed so, milord. And can you tell us what is common to each of these units that has changed direction?"
Again, Lord Reginald beamed with pride. "I can, Holmes! They are the units whose moves bounced in the Spring!"
"Quite right, Lord Reginald! And with this fact, we know all that we need to know. The units have begun the game moving 'up' the alphabet, but whenever any unit 'bounces' in its move, it shall take the alternate direction beginning with its next move. By ordering the units in this way from turn to turn, keeping track of the alphabetical direction that each of them is currently going, we will be able to determine which two neutral centres are the last to be captured. Knowing which centres these are, of course, will allow you to purchase the round-trip ticket for an emissary to be sent to meet with the Sultan."
As my friend and Lord Reginald spoke, though, I had been staring intently at one particular area of the board, and with something like the delight of a bully putting a needle to a toddler's balloon, I softly said, "My dear Holmes, pray tell me please why the Russian fleet in St. Petersburg moved to the Gulf of Bothnia in the Fall."
This took Lord Reginald aback, and he looked at the board with interest and concern. "The good doctor is right, Holmes. Since that fleet bounced in the Spring, it should now be going 'down' the alphabet -- towards 'Z.' Since none of its possible destinations are later in the alphabet than 'St. Petersburg' itself, we proceed from 'Z' to 'A', and the first space we come to should be 'Finland', not 'Gulf of Bothnia'. This seems to defeat the entire theory, Holmes."
Holmes seemed unfazed. "Not at all, my good men. What you have noticed is something quite key to the puzzle. St. Petersburg moves to the Gulf of Bothnia because the map abbreviation for that location -- 'BOT' -- is earlier in the alphabet than the abbreviation for Finland -- 'FIN'."
"Of course!" said Lord Fortescue. "The alphabetisation is by the standard map abbreviation, not by the full placename! I should have known, given the Sultan's consistent use only of abbreviations when supplying us with orders!"
I supplied the final detail. "Now I see what you mean, Holmes, about London not being the final alphabetical build-site for England! England's 1901 build is a fleet in Liverpool, because although 'Liverpool' comes earlier alphabetically than 'London', 'LVP' comes later than 'LON'!"
"Just so, Watson."
With this, Lord Fortescue and I toasted the insight and intelligence of our friend Sherlock Holmes, and thereupon we all sat together and 'played the game forward', watching the neutral centres dwindle in number until the Sultan's riddle was solved. Within the span of an hour or so, the Foreign Secretary was off to purchase a round-trip ticket, and the extension of the deepwater lease on the Port of Suwat was safely assured.
Holmes still has some more tricks up his sleeve! Knowing what you know now, though, can you "play the game forward" and determine where the royal envoy is to be sent, and where the ticket he will use will take him to meet with the Sultan to sign the lease extension? Mail your answers to The Pouch!
-- Dr. John H. Watson
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