PROBLEM CATEGORIES

PROBLEM CATEGORIES

What are the categories of problems based on their solvability?

Based on the ability to solve a problem, we distinguish three categories of problems:

Solvable

They are problems whose solution has been formulated and is already known. Also,  problems whose solution has not yet been formulated, but their relevance to other already solved problems allows us to consider with certainty the possibility of their solution.

For example, the solution of a first-degree equation.

Unresolved

These are problems that have proven to have no solution.

For example, the problem of squaring the circle with a straightedge and compass.

Open

These are problems that have not yet been solved, but have not yet been proven.

that they have no solution so that they can be characterized as unsolvable.

For example, the problem of unifying the four force fields.

What are the categories of solvable problems in terms of the degree of structuring of their solutions?

Based on the degree of structuring of their solutions, solvable problems are divided into  three categories:

Structured

They are problems whose solution comes from an automated process. For example, the solution of the quadratic equation

Semi-structured
They are problems whose solution is sought within the framework of a clearly predefined range of possible solutions.
For example, the choice of a means of transport to go from one place to
another.

Unstructured
They are problems whose solutions cannot be structured or the possibility of their structuring has not been explored in depth. In these problems there are infinite
possibilities for solution at a practical level, while human intuition plays a primary role.
For example, the problem of which products to buy at the supermarket.