This article describes two heuristic strategies for problem solving: the "use of false assumption" strategy and the "use of double false assumption" strategy. Both of these strategies have their roots deep in history. In this article, we define these two strategies and illustrate their use in a problem developed by Frances Pellos. The article provides an overview of occurrences of these two strategies in various mathematical and educational texts. The texts show clearly that both of these strategies played a significant role in mathematics education in the past. We present some examples from concrete historical documents, which we use later for the preparation of a teaching experiment. We also present the conclusions of an experiment conducted on three lower secondary schools in the Czech Republic, the goal of which was to test the applicability of the "use of false assumption" strategy as a propaedeutic to solving word problems using equations.