# Overview

##### Original Research

A BLACK WIDOW OPTIMIZATION ALGORITHM FOR SOLVING KENKEN PROBLEM

#### ALAA MOKHTAR 1, HEGAZY ZAHER 2, and NAGLAA RAGAA 3.

##### Abstract

Kenken is the most famous kind of arithmetic and grid puzzle. Kenken is a grid puzzle like Sudoku. In Kenken, the main objective is to fill cells from 1 to n×n grid on the condition that the mathematical operation on every cage is achieved, so that the main constraint in the kenken problem is to produce a certain “target” number when combined using a specified mathematical operation {+, -, ×, ÷}, under this condition, every number appears once on every column and row. The grids range in size from 3×3 to 9×9. KenKen is a new puzzle phenomenon that’s sweeping the world educational, and fun, KenKen is a great way to exercise your brain and sharpen your mathematical tools at the same time. In this paper, the proposed research used python programming to solve the kenken puzzle by using a heuristic search and a black widow optimization algorithm. The proposed algorithm depends on a heuristic search that used logic rules. A lot of puzzle cases cannot be solved, then the black widow optimization algorithm will be run. Obtained results show the efficiency that the proposed algorithm in grids ranges in size 5×5, 7×7, and 9×9 are more efficient than the old ones.

##### Keywords

Discrete Optimization, Kenken Puzzle, Mathematical Games Analysis, Black Widow Optimization Algorithm.