Strategy optimization for deductive games

Shan Tai Chen, Shun Shii Lin*, Li Te Huang, Sheng Hsuan Hsu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


This paper presents novel algorithms for strategy optimization for deductive games. First, a k-way-branching (KWB) algorithm, taking advantage of a clustering technique, can obtain approximate results effectively. Second, a computer-aided verification algorithm, called the Pigeonhole-principle-based backtracking (PPBB) algorithm, is developed to discover the lower bound of the number of guesses required for the games. These algorithms have been successfully applied to deductive games, Mastermind and "Bulls and Cows." Experimental results show that KWB outperforms previously published approximate strategies. Furthermore, by applying the algorithms, we derive the theorem: 7 guesses are necessary and sufficient for the "Bulls and Cows" in the worst case. These results suggest strategies for other search problems.

Original languageEnglish
Pages (from-to)757-766
Number of pages10
JournalEuropean Journal of Operational Research
Issue number2
Publication statusPublished - 2007 Dec 1


  • Algorithm
  • Bulls and cows
  • Mastermind
  • Pigeonhole principle
  • Search strategies

ASJC Scopus subject areas

  • General Computer Science
  • Modelling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


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