The paper discusses means of representing states of the world which are easily described as pictures of triangles, circles, and squares in horizontal, vertical, or enclosure relationships. The study is oriented to the comparative evaluation of different representations for computer-based question- answering systems. Three languages for representing such pictorial data are constructed. The basic units of the first are pictures, of the second trees, and of the third sentences. Each of the three languages is further modified to serve for describing data, for specifying constructions, for posing queries, and for stating answers. The interrelations among the various specialized uses of these three languages are investigated. Queries are best posed in an English- like language, computer search best proceeds on data represented as trees, and answers can often be best presented in picture representations. Results are in the form of a context-free generative grammars for the different languages expressed as production rules, b theorems showing correspondences between, say, all query sentences and all pictorial answers, and c formulae for the effort to search for answers, for optimal trees to store data.