  Egyptian decompositions of 2/D as a sum of two unit fractions are studied by
means of certain divisors of D, namely r and s. Our analysis does not concern
the method to find r and s, but just why the scribes have chosen a solution
instead of another. A comprehensive approach, unconventional, is developed
which implies having an overview of all pre-calculated alternatives. Difference
s-r is the basis of the classification to be examined before taking the right
decisions, step by step, if difficulties are encountered. An adequate
adjustment of s-r limits the number of all alternatives to 57, what is very
few. A four-component generator (2/3, 2/5, 2/7, 2/11) operates as a (hidden)
mother-table. Adding few logical rules of common sense is enough to explain the
reasons of the Egyptian choices. Even the singular case 2/95, which can not be
decomposed into two fractions but only into three, reveals a doubly justified
explanation.
