Publication Date
10-1-2022
Document Type
Article
Publication Title
Australasian Journal of Combinatorics
Volume
84
First Page
86
Last Page
110
Abstract
For any dimension n ≥ 3, we establish the corner poset, a natural triangular poset structure on the corners of 2-color hypercubes. We use this poset to study a problem motivated by a classical cube stacking puzzle posed by Percy MacMahon as well as Eric Cross’s more recent “Eight Blocks to Madness.” We say that a hypercube is 2-color when each of its facets has one of two colors. Given an arbitrary multiset of 2-color unit n-dimensional hypercubes, we investigate when it is possible to find a submultiset of 2n hypercubes that can be arranged into a larger hypercube of side length 2 with monochrome facets. Through a careful analysis of the poset and its properties, we construct interesting puzzles, find and enumerate solutions, and study the maximum size, S(n), for a puzzle that does not contain a solution. Further, we find bounds on S(n), showing that it grows as Θ(n2n).
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Department
Mathematics and Statistics
Recommended Citation
Ethan Berkove and Jordan Schettler. "The corner poset with an application to an n-dimensional hypercube stacking puzzle" Australasian Journal of Combinatorics (2022): 86-110.
