Holmes pointed out to me that his effort in "The Double Elimination Conundrum" proved only that two powers cannot be eliminated in 1901; not that two powers cannot end that year without a single unit on the board. This was a subtle point, but crucial. After I thought about it, it was clear that a power could go into 1902 without any units on the board and yet still be in the game. The requirement is that all the power's units must be dislodged in Fall of 1901, and the player must then choose to disband them, subsequently waiving all his builds.

"To determine if the game described by the refugee was possible," Holmes began, "the first step is to learn which countries can have all their units dislodged -- those powers for whom all units can be brought adjacent to two foreign units in the opening move of the game.

"Army Liverpool cannot leave our island in Spring of 1901, and the only unit which can be brought adjacent to it is the French fleet Brest. Thus it cannot be disbanded.

"Similarly, Fleet Naples can come into contact only with Fleet Trieste, so we know that Italy also must have some units in 1902.

"Two fleets, London and Edinburgh, can move into the North Sea to come in contact with Fleet Kiel (if it moves to Holland, Denmark, or the Helgoland Bight), but since only one of the English fleets ccan occupy that space, dislodgement of the Kiel fleet is impossible. Similarly, if Kiel opens to the Baltic Sea, it can be threatened only by the St. Petersburg fleet (true, both of the Russian armies could move adjacent to it, but they could not support its dislodgement from the Baltic). If the fleet opens to Berlin, then only the Warsaw army can move adjacent to it. In sum, Kiel cannot be forced into retreat.

"Any of the Turkish units can be dislodged in Fall of 1901, but Ankara and Smyrna only if they open to Armenia. Since both cannot move there at the same time, forced retreat of all Turkish units is also impossible.

"Thus, only Russia or Austria can be forced to retreat all their units in 1901. (We can readily verify that this fate is possible for both of these powers.) We can immediately eliminate Russia, however, since from the builds we know that one country built four armies in 1901: only Russia is able to do this.

"It is thus obvious that Austria must be the power to have disbanded all its units in the retreat phase of Fall 1901."

At this point, Holmes paused to ensure that I was keeping up with him. When I raised my head from the Diplomacy board, having verified his statements, I nodded that he should continue.

"By the end of 1902, each power other than Russia is capable of achieving a maximum size of twelve centres, while Russia may own as many as sixteen. But with the Sultan and the refugee within one centre of each other at that time, we know that, at most, twenty-five of the thirty-four centres are owned; a maximum of twelve by the Sultan, and thirteen for the refugee. Since there are twenty-two home centres, only three neutrals can have been captured. We know from the builds that by the end of 1901, all twenty-five centers were already occupied -- the total of each power's unit-count is twenty-five.

"Only Russia can build four units a year, and so only Russia can reach thirteen centres in 1902. The refugee was therefore Russia, while the Sultan held a twelve centre power after 1902."

This much did seem elementary, as Holmes was fond of saying, but it seems that I will forever need my friend to explain his methods to me. I sighed, and Holmes continued.

"So we know that the Sultan must have played England, France, Germany, Italy, or Turkey. Turkey can be eliminated immediately: one of two Black Sea neutrals would have to fall to Russia to give the refugee his four builds in 1901, leaving only one to be taken by Smyrna or Ankara. Turkey simply cannot grow to six centres in 1901 if Russia gets to eight, and thus Turkey cannot grow to twelve centres by the end of 1902.

"England could, with French help, reach six units in 1901, but having built three armies (as the builds tell us), twelve centres in 1902 is clearly impossible -- there isn't enough time for his own fleets to move to sea, convoy, and return to land, each to gain a new supply centre, in a single year. Likewise Italy."

"The Sultan must therefore have played either Germany or France."

I suppose I will never get used to the way Holmes effortlessly unravels the most intricate of puzzles and makes them seem so very simple. From here, though, it became easy, and I took up the story.

"Ah yes, Holmes, I see! We are told that two powers ended 1901 without any units. You have shown me that one of these powers could do so without being eliminated, and you have proven that in this game it was Austria. So the other power to end 1901 without any units was eliminated in that first year. With 'The Double Elimination Conundrum' fresh in my mind, I recall that the only powers who may be eliminated in the first year are Austria, France, and Germany. Since we know Austria was not eliminated (though he chose to end the year without any units), and since you have proven the Sultan must have played either Germany or France to have achieved a size of twelve centres by the end of 1902, the power that was eliminated in 1901 must have been the other power in the pair, either France or Germany!"

"Yes indeed, Watson, but which one? We turn now to determining which of the two was eliminated: France or Germany? This can be only be deduced by consideration of the fall builds. Austria waived his builds, Russia built four armies, one power (the Sultan's power) built three, and the others had no option -- barring some rather implausible scenarios which need not concern us now, this means they ended 1901 in possession of exactly three supply centres.

"We begin by assuming France was eliminated. England must take Brest for this to happen, and for England to lose a home centre (thus to remain at three centres, as is necessary given the builds) would require a convoy of a German army from Kiel, through the Heligoland Bight and the North Sea, into either London or Edinburgh.

"Since we have assumed that France is eliminated, we must assume that the Sultan played Germany and grew to twelve units by the end of 1902. This means, of course, that he must achieve a gain from each of his initial units, to grow to a size of six centres by the end of the first year. And we have just deduced that, of necessity, one of his 1901 gains must be either Edinburgh or London. Notice what this means, however! The fleet in the Heligoland Bight is busy convoying in Fall, and therefore Germany cannot end 1901 with six centres, so our premise was false...."

I was struggling to keep up. "Which premise was that, Holmes?"

He answered immediately, without even acknowledging the question. "...that England held three centres at the conclusion of the first year. England must keep both London and Edinburgh to allow Germany to reach six centres, and yet must take Brest to eliminate France."

"But Holmes," I interjected. "I thought you had proven that England held only three centres. Russia built four, Austria had disbanded all his units and then waived his builds, and only the Sultan's power -- which you have said is either France or Germany -- has any option to build!"

"Quite right, Watson. So what we have learned is that if France is the eliminated power, England must grow. Since, as you have just recounted, England cannot grow, we are forced to also invalidate our earlier premise -- that France was eliminated in the first year!"

I was not sure I followed his argument, but the consequence was clear. "So now all other possibilities have been eliminated, and the one which remains must be true: Germany was eliminated in 1901!" I exclaimed. "And the Sultan must have been playing France!"

"Quite so, Watson," said Holmes, taking up his pipe.

Back to the puzzle....