It was entitled Solvable and Unsolvable Problems, and first gave an example of a 'solvable' problem. This was a solitaire game (actually the 'fifteen puzzle') in which, as he described, there were only a finite number of possibilities to consider (namely 16! = 20,922,789,888,000). Hence, in principle, the game could be 'solved' simply by listing all the possible positions.
这篇文章题为《可解问题与不可解问题》。图灵首先给出了一个可解问题的例子，这是一个纸牌解谜游戏，具有有限种可能的情况（即16！= 20, 922, 789, 888, 000），理论上可以穷举所有的情况，所以这个游戏是可解的。
This helped to illustrate the nature of an absolutely 'unsolvable' problem, such as he went on to describe, but the large number also demonstrated the gap between theoretical and practical 'solvability'.
As it happened, of course, the Bombe had indeed exploited the finiteness of the Enigma by just such a brute force method, but in general the knowledge that a number is 'only' finite is not of practical significance.
One cannot play chess, nor deduce all the wirings of an Enigma machine, by knowing that the possibilities are finite.
The 'fifteen puzzle', indeed, poses a tough problem to the computer programmer. Turing machines, when embodied in the physical world, are severely limited by considerations other than those of logic.
While some physical quantities (such as temperature) may be described by one number, in general they will require a set of numbers; anything like a direction in space, for instance, will do so.
It is usual to 'index' this set by a letter of the alphabet. From a modern point of view the structure of the set is a reflection of the group of symmetries associated with the physical entity, and it is common to use a different type of letter (e.g. lower-case, upper-case, Greek) when different symmetry groups are implied.
The word 'fount' made this principle explicit.