In this paper we study the Closest String Problem (CSP). To solve the CSP involves finding a string that minimizes the maximum Hamming distance from a given set of strings with an arbitrary alphabet Its decision version is NP-complete. The Hamming distance between two strings a and 6 of equal length is calculated by simply counting the character positions in which a and b differ. In this work we propose two approaches to solve the CSP. The first is a greedy heuristic algorithm (GREEDY), the second is a recursive exact method. The algorithms are compared with an integer programming formulation for CSP. Furthermore, computational experiments in comparison tables will show die effectiveness of the proposed algorithms. © 2020 Charles Babbage Research Centre. All rights reserved.