Discrete Optimal Control of a Class of Match-Stick Puzzles

Ukwu Chukwunenye; Tanko Ishaya; Ladan Umar Ibrahim

doi:https://doi.org/10.14445/22315373/IJMTT-V67I12P511

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 12 | Year 2021 | Article Id. IJMTT-V67I12P511 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I12P511

Discrete Optimal Control of a Class of Match-Stick Puzzles

Ukwu Chukwunenye, Tanko Ishaya, Ladan Umar Ibrahim

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.

Keywords

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

References

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

Citation :

Ukwu Chukwunenye, Tanko Ishaya, Ladan Umar Ibrahim, "Discrete Optimal Control of a Class of Match-Stick Puzzles," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 12, pp. 94-99, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I12P511