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Sherlock Holmes,
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It was on an excessively hot Sunday afternoon that I decided to visit my friend Sherlock Holmes at 221 B, Baker Street. I expected him to be lackluster and morose as he had an aversion to the heat of the Summer, and thought my visit could cheer him up. But to my surprise he was sitting upright at a table dressed with the finest table cloth in the house and a teapot and his best silverware on it, as if expecting important visitors. "Halloa, it's you, Watson! Come in and have a seat. A cup of tea? No, you're not intruding. The company I'm expecting may be here in a minute or in a few hours, but I'd be disappointed if no one shows up before the curtains are drawn." "An unannounced visitor then. And what may be the reason for his or her appearance?" "This letter," said Holmes and tossed me an envelope with the seal broken. "You must recognize the seal." Although it had been a few years since the last challenge, the seal was undeniably that of the Sultan of Suwat. "Has the Sultan challenged the Crown with a new riddle for the extension of the lease on the Port of Suwat, to which the Foreign Office was once again compelled to seek your services?" "Yes and no," replied Holmes mysteriously. "Even though it's a riddle in the sense you describe, it's merely a variation of an old one." "Perhaps he ran out of ideas?" "That would be more likely if he made a point of posting a challenge on a regular basis. But the last few years he has sent nothing. Moreover it's the first time that a challenge was made in Summer. In those parts of the world, it's not the season to travel, and I can't say I disagree with that. But irrespective of that, the Sultan is abroad, as yet again the objective is to locate his present whereabouts in Europe." "Perhaps as he grew older, his habits changed? Half of my clientele are older people with their quirks and whims that were not apparent when they were young. I know none who did not change their customs as the hair thinned and the back curved." "Hm, remember that the Sultan was still a young man when he inherited the throne and sent out the first challenge. He cannot yet be in his fifties now. Old age can therefore not be the cause and the problem in itself betrays a sufficient amount of lucidity to exclude an early form of dementia." Nipping on my tea, I considered this for a moment. "Well, if you'd let me in on the details, perhaps I might understand your concern better." "Certainly. Do you remember the case of the False Start?" "As if I do. I even published a detailed account in the pages of the Diplomatic Pouch." "I'm aware of your rather sensational rendition, including events that had little to do with the case," said Holmes with a sigh. "And so does the Foreign Office. On its strength they came close to a full solution. I was only required to add a small hint to push them over the finish line." I took some delight in the knowledge that my humble writings were read by the highest levels of our great bureaucracy. "So the courier is already on his way?" "By my count he must either already have met the Sultan or be on the verge of doing so. I'm expecting my guests to bring me news of the encounter." Expecting the task to be light, I enquired further. "Well then, what variation did the Sultan propose, that I may match wits with him?" My friend poured some milk in his cup — no sugar — and stirred it with a small, silver spoon before answering. "The main task is still to return the board to the starting situation in the shortest time span possible with no neutral centers taken and no home center occupied by the same unit that started the game there. Furthermore it is still obligatory to maximize the number of dislodgements, but this — and this is important — year by year, not just — or not even — the overall total." "Let me see if I understand this correctly. If the maximum number of dislodgements is known for the first year, then any solution that does not reach that number in its first year, even if the total across two years is superior, is not acceptable." Holmes nodded, and so I continued. "If my memory serves me well, we already had determined that first year maximum. No dislodgements can be made in the first season, while in the second season there can be seven, equal to a third of all units on the board, as each dislodgement involves at a minimum three units. “But wasn't it so that no matter what, this could not lead to a solution in two years, due to the loss of Sevastopol and inability to rebuild a fleet there? But then it will be three years before reaching the initial position. The number of possible moves must grow tremendously!" He added some more milk and stirred again, undisturbed by the hint of despair in my voice. "That's why it's called a variation. The Sultan has invented a novel type of convoy, which apparently has met with great enthusiasm in the clubs and bars of the Port of Suwat. In reference to these origins the rule has been dubbed "portage convoy". In summary this rule allows armies to convoy fleets over land." "An army convoy rule. And what are its features?" "As with standard convoys the convoyed party, the fleet, needs to be on a coast and the end destination must also be a coast. But unlike standard convoys any army, both in landlocked and coastal provinces, can participate in the convoy. The only requirement is that the convoyer is allowed to move to the previous and next territory in the convoy chain. It's furthermore possible for a fleet located on one coast of a multi-coast province to be convoyed to another coast in the same province by an army in any adjacent province. That's about the low and high of it." My tea still too hot for my taste, I blew on it to cool it down. "I see. And this should in some way mitigate the problem of Sevastopol's capture… I get it! As fleets can now be convoyed, or "portaged", over land, Russia could redeem its Southern port with its Northern fleet. Nice. Well, then, all that remains to do is to determine how many dislodgements can be added in the second year to the seven in the first year. Is there again only one retreat?" "No, the number of retreats is limitless. In fact it needs to be maximized." Surprised I blew too hard and the tea nearly spilled out over the edge of the cup. I had to put down my saucer and wipe a drop off my nose before I could look him in the eye. "More than one retreat? Good heavens. Then the Sultan must have correctly deciphered the riddle that you wired to the messenger, inviting him to London, Wales and the Channel islands." "Whether it did, is hard to tell. It could also be that he tried this approach independently and only afterwards understood its meaning. Remember that retreating to London increases the number of dislodgements in that part of the map, a fact that cannot have been overlooked by such an accomplished player as the Sultan." "But if there's more than one retreat, how then can the Sultan's location be determined?" "By virtue of a third condition. Not only is it necessary to maximize the number of dislodgements and the number of valid retreats, but also the total convoy length must be as great as possible." "By convoy length you mean the number of convoyers employed in a single convoy, so that the most basic convoy has a length of one. Does this include standard and portage convoys?" "He did not specify, so we must assume that both types are counted." "And do convoys have precedence over dislodgements?" "No, the conditions were given in order of importance. Dislodgements prevail over retreats, which in turn prevail over convoys." "In that case I fully agree that a retreat to London is more effective than a convoy to Picardy in view of the extra dislodgement in the second year and the increased number of retreats. And how will this help to locate the Sultan?" "According to his message he is sojourning in the province that is the final destination of the only unit that was convoyed more than once." With a grand gesture I put down my empty cup. "Well then, let me solve this riddle forthright."
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