Next Article in Journal
Algorithms and Data Structures for Sparse Polynomial Arithmetic
Previous Article in Journal
Positive Solutions for a Hadamard Fractional p-Laplacian Three-Point Boundary Value Problem
Article Menu
Issue 5 (May) cover image

Export Article

Open AccessArticle

Construction of Fair Dice Pairs

Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
School of Mathematics and Big Data, Guizhou Education University, Guiyang 550018, China
Department of Mathematics, Shanghai University, Shanghai 200444, China
Department of Network Technology, South China Institute of Software Engineering, Guangzhou 510990, China
Department of Mathematics, Changzhou Institute of Technology, Changzhou 213022, China
Author to whom correspondence should be addressed.
Mathematics 2019, 7(5), 440;
Received: 8 April 2019 / Revised: 9 May 2019 / Accepted: 13 May 2019 / Published: 17 May 2019
PDF [290 KB, uploaded 17 May 2019]


An interesting and challenging problem in mathematics is how to construct fair dice pairs. In this paper, by means of decomposing polynomials in a residue class ring and applying the Discrete Fourier Transformation, we present all the 2000 fair dice pairs and their 8 equivalence classes in a four-person game, identifying what we call the mandarin duck property of fair dice pairs. View Full-Text
Keywords: fair dice pairs; discrete Fourier transformation; discrete convolution fair dice pairs; discrete Fourier transformation; discrete convolution
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Huang, Y.; Zeng, Z.; Rao, Y.; Zou, Y.; Wang, Y.; Huang, X. Construction of Fair Dice Pairs. Mathematics 2019, 7, 440.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top