Solution Numbers for the Eight Blocks to Madness puzzle.

Many puzzles with the 30 MacMahon colored cubes have been studied and solved. The original problem is to create a 2 ×2 ×2 model with eight distinct MacMahon cubes to recreate a larger version a specified target cube, also a MacMahon cube, such that touching interior faces are colored the same color. J.H. Conway is credited with arranging the cubes in a 6 ×6 tableau giving a solution to the puzzle. In fact, there are exactly two ways to arrange the eight cubes used to solve the puzzle. We study a less restrictive puzzle, without the requirement of interior face matching, and look not only for solutions to the 2 × 2 × 2 puzzle but also the number of distinct solutions attained for a collection of eight cubes. We also discuss a related question; given a subset of k ≥ 8

MacMahon colored cubes, how many target cubes can be built with cubes from the subset. We will have colored cubes available for puzzling and play! Joint work with Erika Roldan.

Professor Inga Johnson is a topologist, teacher and mentor at Willamette University in Salem, Oregon, USA. She co-wrote the inquiry-based textbook “An Interactive Introduction to Knot Theory” with Allison Henrich. Her research includes articles on knot theory, homotopy theory, topological data analysis and teaching techniques. Inga and co-PI Colin Starr have been awarded two NSF Research Experience for Undergraduates grants that have funded 24 summer projects with

undergraduates.