Fermi problems are often taught in science and engineering as a technique for difficult numerical estimation in which a question is broken down into sub-questions that people can more confidently estimate. Thus, they may be tools providing insight into how people estimate numbers. However, there are no empirical studies into the effectiveness of Fermi problems. This study presented participants with the same questions as both Fermi problems (with sub-questions) and as non-Fermi problems (no sub-questions) and tested the hypothesis that participants’ estimates would be more accurate when presented with Fermi problems than non-Fermi problems. The same data tested a hypothesis that participants would better fit to Benford’s law when presented with Fermi problems than non-Fermi problems. Neither hypothesis was supported, although the strong fit of peoples estimates to Benford’s law was replicated. This first attempt to empirically examine Fermi problems pointed to ways to more rigorously test these hypotheses.

Burns & Krygier (2015) demonstrated that people could exhibit a strong bias towards the smaller first digits, in a way similar to that described by Benford’s law. This paper sought to expand the scope of this phenomenon and to test a possible explanation, the Recognition Hypothesis that a Benford bias is due to life-long environmental exposure to this statistical relationship. Participants completed three numerical tasks: A Generation Task requiring answering trivia questions; a Selection Task requiring selecting between two numerical responses; and an Estimation task requiring estimating the number of jelly beans in a jar. The results found no evidence of any first digit effect in the Recognition Task, some evidence of Benford bias in the Generation Task and strong evidence in the Estimation Task. Future research should focus on alternatives to the Recognition Hypothesis and investigate the parameters of Benford bias in generation tasks