By such work, the pupils (officers) acquired the same kind of skill in solving strategic and tactical problems that a boy acquires in solving problems in arithmetic--a skill in handling the instruments employed. Now the skill acquired in solving any kind of problem, like the skill developed in any art, such as baseball, fencing, or piano-playing, does not give a man skill merely in doing a thing identically like a thing he has done before: such a skill would be useless, for the reason that identical conditions almost never recur, and identical problems are never presented. Similar conditions often recur, however, and similar problems are often presented; and familiarity with any class of conditions or problems imparts skill in meeting any condition or any problem that comes within that class. If, for instance, a man memorizes the sums made by adding together any two of the digits, he is equipped to master any problem of addition; and if he will practise at adding numbers together, he will gradually acquire a certain ability of mind whereby he can add together a long row of figures placed in a sequence he never saw before, and having a sum he never attained before. Or a pianist, having acquired the mastery of the technic of the keyboard and the ability to read music, can sit down before a piano he never sat at before and play off instantly a piece of music he never saw before. Doubtless Moltke had ideas of this kind in mind when his plans for educating strategists and tacticians by problems on paper and by games were ridiculed by the unimaginative, and resisted by the indolent; and certainly no man was ever proved right more gloriously than Moltke. In the war with Austria in 1866, the Prussian army defeated the Austrian at Sadowa or Königgrätz in nineteen days after the declaration of war. In the war with France in 1870, the Prussian army routed the French and received the surrender of Napoleon III in seven weeks and two days, not because of superior courage or experience in war, but by more scientific strategy. As Henderson says: "Even the French generals of divisions and brigades had had more actual experience (in war) than those who led the German army corps. Compared with the German rank and file, a great part of their non-commissioned officers and men were veterans, and veterans who had seen much service. Their chief officers were practically familiar with the methods of moving, supplying, and maneuvering large masses of troops; their marshals were valiant and successful soldiers. And yet the history of modern warfare records no defeats so swift and complete as those of Königgrätz and Sedan. The great host of Austria was shattered in seven weeks; the French Imperial army was destroyed in seven weeks and three days; and to all intents and purposes the resistance they had offered was not much more effective than that of a respectable militia. But both the Austrian and the French armies were organized and trained under the old system.