Sherlock Holmes,
Consulting Diplomat

by Manus Hand,
Master ´┐Żnigmatist


Begone And Back: A Basic Conundrum Deciphered Entirely


The Foreign Secretary Lord Fortescue and I — frequently commenting on how remarkable it was for us to find ourselves reconstructing a game of Diplomacy by "playing it forward" — were amazed by the cunning of the Sultan of Suwat, who had posed this lovely riddle, Begone And Back, to the British government. We were amazed to no less an extent, of course, by the intelligence of our friend Sherlock Holmes, who had deduced the rules of movement and adjustment that the players of this game of Diplomacy must have followed, and who had enlightened us as to these particulars.

As Holmes had explained to us, the pieces in the game that the Sultan described were each following a specific common rule to decide upon their next order. With every unit moving on every single turn — Holmes pointed out that this effectively ensured that no retreats would be possible — the destination of each unit's order was either the adjacent space whose abbreviation was next alphabetically from that of its current location, or which was last alphabetically before it. That is, an army in Munich (MUN) could only ever be ordered either to Ruhr (RUH being the adjacent space next alphabetically later than MUN itself) or to Kiel (KIE, being the adjacent space last alphabetically before MUN itself). Which of these two destinations the unit would choose was wholly dependent on the unit's own movement results leading up to the order. As Holmes explained, every unit in this game begins its life moving up the alphabet, toward A. As an example, the German army that began the game in Munich was indeed ordered to Kiel in Spring of 1901. Units continue moving up the alphabet (toward A) unless and until their movement order fails, and they bounce, at which point that unit changes direction and begins moving down the alphabet (toward Z). Such a "downward" direction is the rule followed by that unit until it again "bounces", failing in its attempt to move, at which point it will once again reverse its alphabetical direction of movement.

Holmes also pointed out to us that the Sultan had made available sufficient evidence — both in the first game-year's worth of moves that he had provided, and also in his rather obscure written clues — for us to know that the units went from one end of the alphabet to another, as necessary. For example, the Turkish fleet beginning the game in Ankara (and moving, like all units on the first turn, toward A) saw itself ordered to Constantinople. This was due to the fact that there are no spaces adjacent to Ankara having an abbreviation earlier in the alphabet than ANK itself, and so the alphabet is "restarted" from Z, as it were, and CON found to be the closest-to-Z (still continuing our movement back "up" to A) space to which the fleet could be ordered.

This much, Lord Reginald and I saw, was borne out by the first two seasons worth of game results, which the Sultan had provided to us. These are reproduced below, with asterisks marking those orders that had bounced, causing the units in question to thereupon "reverse" their alphabetical direction.

SPRING 1901
AUSTRIA
A BUD-VIE *
F TRI-ALB
A VIE-TYR *
ENGLAND
F EDI-CLY
F LON-ENG
A LVP-EDI
FRANCE
F BRE-PIC
A MAR-GAS *
A PAR-GAS *
GERMANY
A BER-SIL
F KIE-HOL
A MUN-KIE
ITALY
F NAP-ION
A ROM-NAP
A VEN-TYR *
RUSSIA
A MOS-LVN *
F SEV-RUM
F STP/SC-LVN *
A WAR-UKR
TURKEY
F ANK-CON *
A CON-BUL
A SMY-CON *
FALL 1901
AUSTRIA
F ALB-ADR
A BUD-GAL
A VIE-BOH
ENGLAND
F CLY-NWG
A EDI-CLY
F ENG-BRE
FRANCE
A MAR-PIE
A PAR-PIC
F PIC-ENG
GERMANY
F HOL-HEL
A KIE-HOL
A SIL-PRU
ITALY
F ION-GRE
A NAP-APU
A VEN-APU
RUSSIA
A MOS-SEV *
F RUM-BUL/EC
F STP/SC-BOT
A UKR-SEV *
TURKEY
F ANK-ARM
A BUL-SER
A SMY-SYR

The only other details needed, and which were of course deduced and supplied by the wondrous mind of my friend Holmes, were the rules to be followed by the powers to determine their actions in the adjustment phases. Here the Sultan's written note was all on which we could depend, but it proved sufficient for Holmes. From that cryptic note, the great detective was able to conclude that any power eligible to build any new unit would build only fleets, and would do so in its build centres in reverse (Z-to-A) alphabetical order. Austria, of course, was limited only to building in Trieste, but France, for example, would build a fleet in Marseilles (MAR) if eligible for a single build, and also a fleet in Brest (BRE) if eligible for more than one build (or, of course, if Marseilles were not available to receive a newly built unit, it being either not vacant, or under the control of a foreign power).

As for removals, Holmes explained that any power called upon to remove any number of units would first remove any or all of its armies, in A-to-Z order according to the abbreviations of their current locations, and only once no armies remained for that power to remove, would remove its fleets in this same A-to-Z order.

Given these rules, the Sultan had challenged us to determine which neutral supply centres were the final two to be acquired by any of the great powers in the game. This knowledge was needed so as to allow the Foreign Secretary to dispatch a messenger to the first of these two locations, where he would purchase a round-trip ticket to the other location, then travel upon this ticket to reach the Sultan, who would sign an extension of the most important lease held by the British government on the deep-water facilities of Port Suwat.

Once we had established these rules of movement and adjustment, the chore of "playing the game forward" was relatively easy, although we had to take care, of course, to remember in which direction (A-to-Z or Z-to-A) each of the units had most recently moved or attempted to move. Doing so, we were able to determine that the game proceeded through 1902 as follows.

WINTER 1901
AUSTRIA
BUD TRI VIE
NO ADJUSTMENTS

ENGLAND
BRE EDI LON LVP
BUILD F LVP

FRANCE
MAR PAR
REMOVE A PIC

GERMANY
BER HOL KIE MUN
BUILD F KIE

ITALY
GRE ROM NAP VEN
BUILD F ROM

RUSSIA
BUL MOS 
SEV STP WAR
BUILD F STP/SC

TURKEY
ANK CON SER SMY
BUILD F SMY

UNOWNED
BEL DEN NWY POR
RUM SPA SWE TUN

SPRING 1902
AUSTRIA
F ADR-VEN
A BOH-GAL *
A GAL-RUM *
ENGLAND
F BRE-PIC
F CLY-LVP
F LVP-IRI
A NWG-NTH
FRANCE
F ENG-BRE
A PIE-TUS
GERMANY
F HEL-DEN
A HOL-BEL
F KIE-HOL
A PRU-LVN *
ITALY
F GRE-BUL/SC *
A NAP-ROM *
F ROM-NAP *
A VEN-TYR
RUSSIA
A BOT-FIN
F BUL/EC-BLA *
A MOS-LVN *
F STP/SC-LVN *
A UKR-WAR
TURKEY
F ARM-BLA *
A SER-RUM *
F SMY-EAS
A SYR-ARM *
FALL 1902
AUSTRIA
A BOH-VIE
A GAL-BUD
F VEN-TRI *
ENGLAND
F IRI-ENG *
A LVP-EDI
F NTH-LON
F PIC-ENG *
FRANCE
F BRE-PIC *
A TUS-VEN *
GERMANY
A BEL-RUH
F DEN-BAL
F HOL-HEL
A PRU-SIL
ITALY
F GRE-ION
A NAP-APU
F ROM-TUS *
A TYR-TRI *
RUSSIA
F BUL/EC-CON
F FIN-STP/SC
A MOS-SEV
F STP/SC-BOT
A WAR-GAL
TURKEY
F ARM-ANK
F EAS-AEG
A SER-TRI *
A SYR-SMY
WINTER 1902
AUSTRIA
BUD TRI VEN VIE
BUILD F TRI

ENGLAND
EDI LON LVP
REMOVE A EDI

FRANCE
BRE MAR PAR
BUILD F MAR

GERMANY
BER HOL KIE MUN
NO ADJUSTMENTS

ITALY
GRE ROM NAP
REMOVE A APU

RUSSIA
BUL CON MOS 
SEV STP WAR
BUILD WAIVED

TURKEY
ANK SER SMY
REMOVE A SER

UNOWNED
BEL DEN NWY POR
RUM SPA SWE TUN

As Lord Reginald and I determined and gave effect to the adjustment orders, we expressed our disappointment to have found that absolutely none of the centres that had remained unconquered going into this second game-year had lost their neutral status during the year. Just as was the situation after the moves of 1901 (which the Sultan had provided to us), there yet remained eight unowned neutral centres. "Holmes," I asked, "are you quite certain that we are proceeding correctly?"

"Indeed, doctor, 1902 was rather uneventful for the neutral centres; that is true. Pray continue to the next game-year, however, for we are most certainly following the proper instructions," came my friend's answer, issued after sipping from his snifter of brandy.

SPRING 1903
AUSTRIA
A BUD-VIE
F TRI-ALB
F VEN-ADR
A VIE-TYR
ENGLAND
F IRI-LVP
F LON-ENG *
F PIC-BEL
FRANCE
F BRE-ENG *
F MAR-LYO
A TUS-ROM *
GERMANY
F BAL-SWE
F HEL-DEN
A RUH-MUN
A SIL-WAR
ITALY
F ION-NAP *
F ROM-NAP *
A TYR-VEN
RUSSIA
F BOT-FIN
F CON-SMY *
A GAL-RUM
A SEV-UKR
F STP/SC-BOT
TURKEY
F AEG-SMY *
F ANK-CON *
A SMY-CON *
FALL 1903
AUSTRIA
F ADR-ALB *
F ALB-ADR *
A TYR-TRI
A VIE-TYR
ENGLAND
F BEL-ENG
F LON-NTH
F LVP-NAO
FRANCE
F BRE-PIC
F LYO-WES
A TUS-VEN
GERMANY
F DEN-BAL
A MUN-KIE
F SWE-SKA
A WAR-GAL
ITALY
F ION-GRE
F ROM-TUS
A VEN-APU
RUSSIA
A UKR-WAR
A RUM-SER
F CON-BUL/SC *
F BOT-FIN
F FIN-STP/SC
TURKEY
A SMY-SYR
F ANK-ARM
F AEG-BUL/SC
WINTER 1903
AUSTRIA
BUD TRI VIE
REMOVE A TRI

ENGLAND
EDI LON LVP
NO ADJUSTMENTS

FRANCE
BRE MAR PAR VEN
BUILD F MAR

GERMANY
BER HOL KIE MUN
NO ADJUSTMENTS

ITALY
GRE ROM NAP
NO ADJUSTMENTS

RUSSIA
BUL CON MOS SER
SEV STP WAR
BUILD F SEV

TURKEY
ANK SMY
REMOVE A SYR

UNOWNED
BEL DEN NWY POR
RUM SPA SWE TUN

Once more, Lord Reginald and I felt that our labour to "play the game forward" another year was left unrewarded, for still there remained eight neutral supply centres. This time, it was Lord Reginald who voiced our shared concern. "Holmes, are you quite certain that we shall reach a satisfactory solution to this perplexing riddle? We have now taken the game two years into its future, and not another single neutral centre has been captured."

Our friend was no less positive than earlier he had been. "We can be assured, milord, that we are on the correct course, and that the neutral centres must eventually fall." As he paused to light his pipe, I could tell from his look that the great detective had used his mind's eye to see the next couple of movements for at least some of the pieces on the board. "Proceed, gentlemen, through 1904, and I believe you will find yourselves less disappointed in our progress."

The reader will not be surprised to learn that my friend Holmes was of course correct, as proven by the next sets of orders, which we found to be as shown below.

SPRING 1904
AUSTRIA
F ADR-VEN
F ALB-GRE
A TYR-TRI *
ENGLAND
F ENG-IRI
F NAO-NWG *
F NTH-NWG *
FRANCE
F MAR-LYO
F PIC-ENG
A VEN-APU
F WES-TYS *
GERMANY
F BAL-SWE
A GAL-RUM *
A KIE-HOL
F SKA-NWY
ITALY
A APU-NAP
F GRE-BUL/SC
F TUS-TYS *
RUSSIA
F CON-SMY *
F FIN-STP/SC
A SER-TRI *
F SEV-RUM *
F STP/SC-BOT
A WAR-GAL *
TURKEY
F AEG-SMY *
F ARM-BLA
FALL 1904
AUSTRIA
F GRE-ION
A TYR-VEN
F VEN-TRI
ENGLAND
F IRI-LVP
F NAO-MAO
F NTH-LON
FRANCE
A APU-NAP *
F ENG-BRE
F LYO-WES *
F WES-LYO *
GERMANY
A GAL-BUD
A HOL-BEL
F NWY-NWG
F SWE-SKA
ITALY
A NAP-ROM *
F BUL/SC-AEG *
F TUS-ROM *
RUSSIA
F BOT-FIN
F CON-BUL/SC *
A SER-RUM
F SEV-ARM
F STP/SC-BOT
A WAR-UKR
TURKEY
F BLA-BUL/EC *
F AEG-BUL/SC *
WINTER 1904
AUSTRIA
TRI VEN VIE
NO ADJUSTMENTS

ENGLAND
EDI LON LVP
NO ADJUSTMENTS

FRANCE
BRE MAR PAR
REMOVE A APU

GERMANY
BEL BER BUD HOL 
KIE MUN
BUILD F BER
BUILD F KIE

ITALY
BUL GRE ROM NAP
BUILD F ROM

RUSSIA
CON MOS RUM SER
SEV STP WAR
BUILD F STP/SC

TURKEY
ANK SMY
NO ADJUSTMENTS

UNOWNED
DEN NWY POR
SPA SWE TUN

"At last!" I exclaimed as we reënacted the 1904 Fall Movement orders. "We finally have made some progress against this puzzle! Both Belgium and Rumania have fallen to the Great Powers!"

"Excellent, Watson. The solution is that much clearer, is it not?" asked Holmes.

Lord Reginald, also elated by this turn of events, excitedly began determining the orders to be issued in 1905, which we thereupon made, and which are reproduced below.

SPRING 1905
AUSTRIA
F ION-NAP *
F TRI-ALB
A VEN-APU *
ENGLAND
F LON-ENG
F LVP-NAO
F MAO-IRI
FRANCE
F BRE-PIC
F LYO-MAR
F WES-TYS *
GERMANY
A BEL-RUH
F BER-BAL
A BUD-VIE
F KIE-HOL
F NWG-NTH
F SKA-NWY
ITALY
F BUL/SC-CON *
A NAP-APU *
F ROM-NAP *
F TUS-TYS *
RUSSIA
F ARM-BLA *
F BOT-FIN
F CON-SMY *
F FIN-STP/SC
F STP/SC-LVN
A RUM-GAL
A UKR-SEV
TURKEY
F AEG-SMY *
F BLA-ARM *
FALL 1905
AUSTRIA
F ALB-ADR
F ION-GRE
A VEN-TYR *
ENGLAND
F ENG-BRE
F IRI-ENG *
F NAO-NWG *
FRANCE
F MAR-PIE
F PIC-ENG *
F WES-LYO
GERMANY
F BAL-SWE
F HOL-HEL
F NTH-LON
F NWY-NWG *
A RUH-MUN
A VIE-TYR *
ITALY
F BUL/SC-AEG *
A NAP-ROM *
F ROM-TUS *
F TUS-ROM *
RUSSIA
F ARM-ANK
F CON-BUL/SC *
F FIN-STP/SC *
A GAL-BUD
F LVN-BOT *
A SEV-RUM
F STP/SC-BOT *
TURKEY
F BLA-BUL/EC *
F AEG-BUL/SC *
WINTER 1905
AUSTRIA
TRI GRE VEN
NO ADJUSTMENTS

ENGLAND
BRE EDI LVP
NO ADJUSTMENTS

FRANCE
MAR PAR
REMOVE F LYO

GERMANY
BEL BER HOL KIE
LON MUN NWY SWE
VIE
BUILD F BER
BUILD F KIE
BUILD WAIVED

ITALY
BUL ROM NAP
REMOVE A NAP

RUSSIA
ANK BUD CON MOS
RUM SER
SEV STP
WAR
BUILD F SEV
BUILD WAIVED

TURKEY
SMY
REMOVE F AEG

UNOWNED
DEN POR SPA TUN

As with those of the previous game-year, I was ecstatic with these results. "Both Norway and Sweden fell to the German, Holmes! Another two neutral centres taken! Hopefully this most excellent pace will continue!"

Lord Reginald was just as enthusiastic as I was about this turn of events. "Agreed, doctor! Only four centres remain untaken, Holmes! Eight down, and four left to go!"

Holmes himself, at this point, took a lingering look at the position of the pieces, and then simply hummed in that way that he has, indicating that he knows something more than he wishes to let on. Being of long acquaintance with him, I knew that behind his smiling eyes, he was holding some knowledge that the Foreign Secretary and I had yet to divine. Apparently there was something that our lesser minds had missed, or had misstated, but Holmes, settling contentedly into an easy chair with his pipe and the air of someone whose task is completely done, merely waved his hand at us. "It's onward to 1906 then, gentlemen!" said Holmes. "You seem to have matters quite well in hand now."

So it was; with Holmes having opened a book taken from the shelf, and on occasion idly rearranging the fronds of a potted fern near his easy chair, Lord Reginald and I "played the game forward" yet another year.

SPRING 1906
AUSTRIA
F ADR-VEN
F GRE-BUL/SC *
A VEN-APU
ENGLAND
F BRE-PIC
F IRI-LVP
F NAO-MAO
FRANCE
F PIC-BEL
F PIE-TUS
GERMANY
F BER-BAL
F HEL-DEN
F KIE-HOL
F LON-ENG
A MUN-KIR
F NWY-SKA *
F SWE-SKA *
A VIE-BOH
ITALY
F BUL/SC-CON *
F ROM-NAP
F TUS-TYS
RUSSIA
F ANK-CON *
A BUD-VIE
F CON-SMY
F FIN-BOT
F LVN-PRU
A RUM-GAL
F SEV-RUM
F STP/SC-LVN
TURKEY
F BLA-ARM
FALL 1906
AUSTRIA
A APU-NAP *
F GRE-ION *
F VEN-TRI
ENGLAND
F LVP-NAO
F MAO-IRI
F PIC-ENG *
FRANCE
F BEL-ENG *
F TUS-TYS
GERMANY
F BAL-SWE *
A BOH-GAL
F DEN-BAL *
F ENG-BRE
F HOL-HEL
A KIE-HOL
F NWY-NWG
F SWE-BAL *
ITALY
F BUL/SC-AEG
F NAP-ION *
F TYS-WES
RUSSIA
F ANK-ARM *
F BOT-BAL *
A GAL-BUD
F LVN-BOT *
F PRU-BAL *
F RUM-BUL/EC
F SMY-SYR
A VIE-TYR
TURKEY
F AEM-ANK *
SITUATION IN ADVANCE OF WINTER 1906
AUSTRIA
TRI GRE VEN
NO ADJUSTMENTS

ENGLAND
EDI LVP
MUST REMOVE 1

FRANCE
BEL MAR PAR
MAY BUILD 1

GERMANY
BER BRE DEN HOL
KIE LON MUN NWY
SWE VIE
MAY BUILD 2

ITALY
ROM NAP
MUST REMOVE 1

RUSSIA
ANK BUD BUL CON
MOS RUM SER SEV
STP WAR
MAY BUILD 2

TURKEY
SMY
NO ADJUSTMENTS

UNOWNED
POR SPA TUN

"Most excellent, doctor! The neutral centres continue to drop in number!" said Lord Fortescue as we completed the Fall movement. "The conquest of Denmark by Germany takes us that much further toward the solution!"

"Indeed," I agreed, "although unfortunately only a single centre has this year come under the control of the Great Powers, rather than two as we have seen earlier. Still in all, it is progress, milord."

The Foreign Secretary and I thereupon set about determining the next adjustment orders, but it was at this point that we were interrupted by Holmes who, hearing our conversation, rose from his chair and rejoined us. "Ah, Watson, how wrong you are that the loss of but a single centre is unfortunate. Rather, I would have said it to be a happy foregone conclusion." Smiling, he continued. "Lord Reginald, I presume you are in a rush now to set about meeting the Sultan's terms to extend the important lease. Might I fetch your hat and coat for you?"

Our guest stood as dumbfounded as I, as we both stared blankly at Holmes. At length, Lord Reginald managed to sputter, "Surely, Holmes, you have not had a fair look at the board. The good doctor and I have now 'played the game forward', as you say, merely to the point where there are three neutral supply centres yet to be taken."

"Indeed so, Lord Secretary. Well done to you both. Now, as to your coat and hat...."

Again, Lord Fortescue and I exchanged puzzled glances. "Holmes," I said, "perhaps I am under a misapprehension as to the requirements of the puzzle, for it certainly does not seem that we have in any way yet discovered any information that can be employed to advantage by the Foreign Office. Pray tell, is our task not to determine the final two neutral supply centres that shall lose their neutrality in this game?"

"That is precisely true, Watson. Now that you have done exactly that, I simply assumed that Lord Reginald would wish to take the necessary diplomatic action with some urgency."

"Pardon me, Holmes," said Lord Reginald, "but it seems rather apparent to me that with three supply centres still holding neutral status in this game, it must be impossible at this time to determine which centres will be the two that are finally taken."

While Holmes once more busied himself drawing deeply from his pipe as he re-lit it with some difficulty, I felt compelled to buttress the Foreign Secretary's statement. "Lord Reginald is entirely correct, Holmes. With three centres yet to be conquered, there is positively no way in which we can we know which two centres are the last to fall, let alone the order in which these two will fall, which I understand to be another important detail with which we must concern ourselves."

"Gentlemen," Holmes began, seating himself at the table with us, "you do not give your work enough credit. You have in fact gathered all the evidence needed to answer the Sultan's riddle. Surely you see that."

"Surely we do not!" I nearly exploded, while Lord Reginald nodded in agreement with me.

How about you? Do you know enough to answer the Sultan's riddle yet? Consider the position that has been reached, and see if you realize what it is that Sherlock Holmes realizes. Only when you are ready to do so, click here to read the rest of Dr Watson's account, and Holmes's final solution to this mystery.

— Dr John H. Watson
via Manus Hand
([email protected])

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