This paper considers the discrete search problem for a single lost target by using multiple sensors. The lost target either located in one of a finite set of different states (cells) or moved through them according to random process with discrete time and discrete state space. A search effort at each fixed number of time intervals is a random variable with a given distribution. The probability that the target in a certain state j at a certain time i and the detection function is supposed to be known to the searchers. We seek for the optimal distribution of the effort that minimises the probability of undetection the target over the set of possible different states. Our aim is to deduce an explicit formula for the random distribution of the random variable effort. An algorithm is constructed for obtaining this optimal solution. The effectiveness of this method is illustrated using some examples with numerical results.