Discrete Optimal Control of a Class of Match-Stick Puzzles

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2021 by IJMTT Journal
Volume-67 Issue-12
Year of Publication : 2021
Authors : Ukwu Chukwunenye, Tanko Ishaya, Ladan Umar Ibrahim
  10.14445/22315373/IJMTT-V67I12P511

MLA

MLA Style: Ukwu Chukwunenye, Tanko Ishaya, Ladan Umar Ibrahim "Discrete Optimal Control of a Class of Match-Stick Puzzles" International Journal of Mathematics Trends and Technology 67.12 (2021):94-99. 

APA Style: Ukwu Chukwunenye, Tanko Ishaya, Ladan Umar Ibrahim(2021). Discrete Optimal Control of a Class of Match-Stick Puzzles International Journal of Mathematics Trends and Technology, 67(12), 94-99.

Abstract
This article formulated and obtained unprecedented analytic solutions to a class of relevant problems in a twoperson match-stick games. The proofs, which were accomplished using well-crafted mnemonically efficient notations, settheoretic notions, the greatest and the least integer functions, established the certainty of victory for the starting player if and only if (N-1) is not a multiple of ( M + 1), where M and N are arbitrary maximum match-stick pick size and match-stick availability, respectively, provided the specified optimal strategy is adopted. The article also proved robustly that the condition ( N - 2) ≠ M ( mod(M + 1)) is imperative for first-pick feasibility, based on the optimal policy. Finally the winning strategy was illustrated for some problem instances. 

Reference

[1] L.W. Winston, Operations Research: Applications and Algorithms, Duxbury Press, Boston (2004) 961-962.

Keywords : Availability, Feasibility, Imperative, Optimal, Pick-size, Policy, Recursions.