The skill of individual officers in solving the problems was noted and recorded; and the problems themselves, as time went on and experience was gained, were made more and more to conform to probable situations in future wars with Austria, France, and other countries, actual maps being used, and the exact nature and magnitude of every factor in each problem being precisely stated.
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 Koeniggraetz in nineteen days after the declaration of war.