Two Eliminations In 1901?

"Why impossible, Holmes?" I asked. "I've never seen it happen, and it might be very unlikely, but it seems as though, cooperating in their own demise, it should be at least possible for two powers to be eliminated in the first year."

"Watson, Watson, illogical as ever! 'It seems as though'! Think, man! In affairs of this sort, logic, not emotion, not 'seeming,' should govern us. Now let us think, and leave seeming behind.

"In considering the possible events in 1901, observe first that no fleet can end the year more than two spaces from where it began; that no army can do so, either, unless it is convoyed; and that no convoy can take place in the Spring (since all the fleets begin in coastal provinces and a fleet in a coastal province cannot convoy). These things being so, let us focus and clarify our thinking on the point by asking ourselves this question --

"Which individual powers can be eliminated in 1901?

"First, it is most easily seen that Russia cannot suffer a first-year elimination, since it is impossible to convoy into landlocked Moscow, and no foreign unit begins the year within two spaces of Moscow.

"Neither, secondly, can Turkey be. Smyrna is completely unreachable in 1901 by foreign units; no unit sets up close enough to reach it by land, and no fleet can reach the necessary convoying position in the Aegean Sea (or the Eastern Mediterranean) in the Spring.

"Nor, as a third, can England. A foreign army would have to arrive in Liverpool by convoy in the Fall -- but no fleet of any nationality can reach either the North Atlantic Ocean or the Irish Sea in the Spring, and so no Fall convoy into Liverpool is possible.

"Fourthly, Italy is safe. Foreign armies would have to convoy into both Rome and Naples in the Fall (since none starts close enough to reach either SC by land), requiring the presence of convoying fleets both in the Tyrrhenian Sea and in the Ionian Sea. But the only fleet that could reach either province is the one from Naples, which could convoy an army into at most one of them; so Rome and Naples cannot both be taken."

I was flabbergasted. "Holmes, this is excellent! It seems so simple when you explain your reasoning, but I'm sure I never could have deduced what you conclude so easily. What about the remaining powers, though -- France, Germany, and Austria?"

"The odd fact about them, Watson, is that any one of them might be eliminated in 1901, but no two of them can be. Follow closely.

"France can be eliminated -- either the Liverpool army or the London fleet could reach Brest, for instance (as, in fact, could either German army); the army from Munich can take Paris; and Marseilles is in range both from Venice and from Munich.

"Austria could be eliminated. Vienna can be taken from Munich, Venice, or Warsaw; Budapest from Venice or Warsaw; and Trieste from Rome, Venice, or Munich.

"And Germany could be eliminated as well. Paris, Marseilles, Venice, or Vienna could any one of them reach Munich; Kiel can be taken by any of the armies beginning in Moscow, Warsaw, Liverpool, or Paris; and (even given that the German fleet is busy convoying an army into Kiel) Berlin is still within range of Warsaw.

"So the only powers susceptible to elimination in 1901 are France, Austria, and Germany. But, as I said, no two of them can be eliminated -- we see this by considering the three 'in pairs' as it were.

"The only unit that can capture Paris is the German army from Munich. So either France or Germany will hold Paris at the end of the year; and so France and Germany cannot both be eliminated in 1901.

"Germany and Austria cannot both be eliminated. The only non-German units that can capture Vienna and Budapest are the armies that start in Warsaw and Venice. (Munich is out of the question as a conquering army, of course, since we are trying to find a way to eliminate Germany as well as Austria.) So the Warsaw army must end the year in an Austrian SC -- but then no other unit could take Berlin, unless it were convoyed there by the German fleet (the only fleet that can move into the Baltic Sea in the Spring and so be able to convoy an army to Berlin in the Fall). But if the German fleet is convoying into Berlin, there remains no way to convoy an army into Kiel; either Kiel or Berlin must remain untaken; and Germany is not eliminated.

"Finally, it is impossible that France and Austria should both be eliminated. Since Munich must go to Paris, only Venice is left to capture Marseilles. But that would leave the Warsaw army as the only foreign unit within range of either Vienna or Budapest; and so one or the other must remain untaken.

"And so we see, Watson, that no two powers can be eliminated in 1901."

Back to the puzzle....