Mrs Hudson had scarcely removed the tea and cake plate from the table when Holmes had the Diplomacy board out and started throwing English armies into Scotland. "If you have a moment, Watson, I would be happy to illustrate for you my methods in resolving what you have called The Case of the Absent Professor."
"Indeed, Holmes," came my reply. "I would be most grateful."
"Well Watson, unfortunate and careless as you were in this game, there is a certain perverse elegance to it. Why did you place six armies in England, for example?"
I pointed out that one can never be too careful with one's home country. Holmes continued his narrative:
"From the large number of units you held, Watson, it is clear that you must be trapped, and unable to support yourself in an attack on the blockage causing the trap. Where do such traps exist? Obviously in England and North Africa where six and two armies can be stranded. Five armies in Turkey can be held by unsupported units in Bulgaria and Sevastopol and five in Scandinavia can also be held by three in Kiel, Livonia, and Moscow. Thus, five unsupported units can blockade eighteen allied armies.
"Since neither you nor Codlington could dislodge one another, it seemed you must each occupy separate areas. But this gave a problem since no combination of six, five, five and two adds to your reported fourteen units. A pipe later and I had it: you could occupy Denmark and Codlington the rest of Scandinavia since Denmark adjoins only Sweden. This way, Codlington has four armies and you are both stuck.
"Codlington has builds outstanding, and as you had respected his centres I presumed he was not playing England or Turkey. Furthermore, the absent player must own Kiel, Moscow, Bulgaria, Sevastopol and one other centre. Only if that other were Warsaw, and Codlington was Russia, would he be unable to build."
"Amazing, Holmes! Your powers of deduction are truly astounding to me. What surprises me more is that you claim the line could be held with one fewer unit? Pray, show me how this could be!"
"To blockade using one fewer unit, one need only observe that if Codlington had a fleet on the north coast of St. Petersburg it could not move southward. Thus we might consider the possibility of dispensing with the Moscow and Livonia armies and building the stalemate line with four units. However, the problem is...."
For once, I saw the flaw in Holmes' argument. "No Holmes, you go too far, for in that case Codlington could order St. Petersburg to Norway, Norway to Finland, Finland to St. Petersburg, and then escape! Nor could you stop the fleet escaping to Norway, since it could be supported from Sweden! Even you can't stop a supported move with a single unit."
"Ah, but I can, Watson, when the supported move cannot succeed without an impossible dislodgement. The Turk could not have left all of his units to fall into civil disorder by simply exiting the Calhamer Club as he did, but all that is necessary to prevent an escape from this position" -- Holmes removed the Moscow and Livonia armies and placed a Turkish fleet in the Barents Sea -- "is a perpetual order for the Barents Sea fleet to move to St. Petersburg."
Disbelieving, I stared at Holmes' handiwork. Eventually, I had to agree with him that Codlington and I would have been equally trapped by this arrangement as well!
It is somehow reassuring to know that as clever as the dastardly Professor Moriarty can be, Sherlock Holmes can be counted upon to one-up him.
-- Dr. John H. Watson
via Graeme Ackland
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