The ancient Egyptians developed original and simple methods to solve many mathematical problems. But to understand this, one must be careful not to project our own algebra system backwards in time. First, we point out that they knew the false position method, as is demonstrated not only by four problems in the Rhind papyrus, but also by two more ancient problems from papyrus Berlin 6619 (we propose a new wording for one of them). Second, we highlight by means of four problems – two from the Moscow papyrus and two from the Rhind papyrus – that this method was part of a much larger heuristic process.