Playing Mastermind with Wordle-like Feedback

Abstract

We introduce an extension of Mastermind called Clear Mastermind with enhanced feedback inspired by that from Wordle. The only difference between Clear Mastermind and Mastermind is a rule that provides more precise feedback, as found in Wordle. In Clear Mastermind, the feedback contains the positions of the colors the codebreaker guessed correctly and the positions of colors that appear in the answer but in different positions. We explore the fewest number of guesses that a codebreaker requires to find the answer in Clear Mastermind according to its two parameters: the number of colors and the length of the answer.

MSC:

• 05-08
• 05A05

Acknowledgment

The authors would like to thank their supervisor, Professor Liang Yu, for his insightful suggestions and encouragement. He pointed out some mistakes in a previous version of the paper and guided the authors to find another elegant and accurate proof. The authors also extend their sincere thanks to the anonymous referees for their constructive suggestions that led to a significant improvement of the paper.

Disclosure Statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Renyuan Li

RENYUAN LI entered National University of Singapore in 2023, to pursue a Ph.D. in ISEM. Before that, he obtained his bachelor of science in statistics at Nanjing University.

Department of Industrial Systems Engineering and Management, National University of Singapore, Singapore 117576, Singapore

[email protected]

Shenglong Zhu

SHENGLONG ZHU received his bachelor of science in mathematics and applied mathematics from Nanjing University in 2023. He went on to pursue an academic master degree in mathematics at Nanjing University.

Mathematical Department, Nanjing University, Nanjing City, Jiangsu Province 210093, People’s Republic of China

[email protected]