Abstract
<p>This article introduces a novel visual reasoning task suitable for any course in which critical thinking, reasoning under uncertainty, or the principles of scientific explanation are curricular goals. The task presents colored geometric shapes as unknown numerical values across four equations. It is intentionally designed not to have a unique mathematical solution: it is underdetermined, and its purpose is to probe whether solvers can identify the most parsimonious explanation — the one that accounts for all the data with the fewest assumptions. This design principle draws on Occam’s razor as formalized in the philosophy of science (Sober, 2015) and on Dawkins’s (2009) Explanation Ratio, which defines the power of a theory as the ratio of what it explains to what it must assume. Fifty-three voluntary respondents ranging in age from 15 to 62, from diverse cultural and professional backgrounds, produced twelve distinct solutions classifiable into six reasoning profiles. Only 19% identified the most parsimonious solution; the majority patched or abandoned their initial rule rather than revising it. The article describes each profile, connects them to three core cognitive biases, and provides a structured facilitation guide for deploying the task across secondary school, undergraduate, and graduate courses in any discipline.</p>