Finding combinations of four-operations with Type-2 tree structure

Özkul E., Tiryaki B. K., Tezel Ö., Ağayev E., Kesemen O.

Pamukkale University Journal of Engineering Sciences, vol.27, no.1, pp.52-59, 2021 (ESCI)


Combination problems are one of the most important issues of probability theory. The four-operations combination problem underlies the basis of some competition programs broadcasted in many national channels. In these competition programs, the competitors are expected to reach the target number by using six numbers and four basic arithmetic operators. The numbers are used at most once, the operators can be used any desired number to reach the target number. In this problem, all four-operations combinations include the operation blocks consisting of two numbers and an operator. Therefore, the four-operations combination problem is solved by developing a "Type-2 Tree Structure" which is a new approach to accurately model the operation blocks. The performance of the proposed method for the four-operations combination problem is examined by a simulation study. Also, the statistics from experimental results are given in this study.