Here's one way to see that the pattern holds regardless of the grid configuration.

Let's say an explosion takes place in cell c at time t = 5. That explosion would have wiped out c along with all of c's neighbors. Because we wiped out all of the neighbors, there's nothing left to stop the next bomb at c from going off four seconds later, at t = 9.

So more generally, once an explosion takes place in a cell, that cell is guaranteed to explode every 4 seconds from then on.

The first explosion takes place at t = 3. So that's why we repeat once we reach 3 seconds.

import java.io.; import java.math.; import java.security.; import java.text.; import java.util.; import java.util.concurrent.; import java.util.regex.*;

public class Solution {

// Complete the bomberMan function below.
static String[] bomberMan(int n, String[] grid) {
    String[] ans = new String[grid.length];
    int aa = grid[0].length();
    String ab = "";
    //String[] grd = new String(grid.length);
    for(int i=0;i<aa;i++){
        ab = ab.concat("0");
    }

    if(n%2 == 0){
        for(int i=0;i<grid.length;i++){
            ans[i] = ab;
        }
    }
    else{
        if(n==1){
            ans = grid;
        }
        else{
            int count = 0;
            while(count<2){ 
            for(int i=0;i<grid.length;i++){
                char[] tmp1 = grid[i].toCharArray();
                for(int j=0;j<aa;j++){
                    if(tmp1[j] == 'O'){
                        tmp1[j] = '1';
                    }
                    else if(tmp1[j] == '.'){
                        tmp1[j] = 'O';
                    }
                }
                String ala = new String(tmp1);
                grid[i]=ala;
            }
            int flag = 0;
            int flag1 = 0;
            for(int i=0;i<grid.length;i++){
                char[] tmp = grid[i].toCharArray();
                char[] tm2 = grid[i].toCharArray();
                char[] tm3 = grid[i].toCharArray();
                if(i-1 != -1){
                    tm2 = grid[i-1].toCharArray();
                }
                else{
                    flag = 1;
                }
                if(i+1 != grid.length){
                    tm3 = grid[i+1].toCharArray();
                }
                else{
                    flag1 = 1;
                }
                for(int j=0;j<aa;j++){
                    if(flag == 0 && flag1 == 0){
                        if(tmp[j] == '1'){
                            tmp[j] = '.';
                            if(j!=0){
                                 tmp[j-1] = '.';
                             }
                            if(j!=tmp.length-1){
                                 if(tmp[j+1] == 'O'){
                                     tmp[j+1] = '.';
                                 }
                             }
                            if(tm3[j] == 'O'){
                                 tm3[j] = '.';
                             }
                            if(tm2[j] == 'O'){
                                 tm2[j] = '.';
                             }
                        }
                    } 
                    else if(flag == 1 && flag1 == 0){
                         //flag = 0;
                         if(tmp[j] == '1'){
                             tmp[j]='.';
                             if(j!=0){
                                 tmp[j-1] = '.';
                             }
                             if(j!=tmp.length-1){
                                 if(tmp[j+1] == 'O'){
                                     tmp[j+1] = '.';
                                 }
                             }
                             if(tm3[j] == 'O'){
                                 tm3[j] = '.';
                             }
                         }
                     }
                    else if(flag1 == 1 && flag == 0){
                        //flag1 = 0;
                        if(tmp[j] == '1'){
                             tmp[j]='.';
                             if(j!=0){
                                 tmp[j-1] = '.';
                             }
                             if(j!=tmp.length-1){
                                 if(tmp[j+1] == 'O'){
                                     tmp[j+1] = '.';
                                 }
                             }
                             if(tm2[j] == 'O'){
                                 tm2[j] = '.';
                             }
                         }
                    }
                    else{
                        if(tmp[j] == '1'){
                             tmp[j]='.';
                             if(j!=0){
                                 tmp[j-1] = '.';
                             }
                             if(j!=tmp.length-1){
                                 if(tmp[j+1] == 'O'){
                                     tmp[j+1] = '.';
                                 }
                             }
                         }
                    }
                }
                String a3 = new String(tmp);
                grid[i] = a3;
                if(flag == 0 && flag1 == 0){
                    String a1 = new String(tm2);
                    String a2 = new String(tm3);
                    grid[i-1] = a1;
                    grid[i+1] = a2;
                }
                else if(flag == 1 && flag1 == 0){
                    //String a1 = new String(tm2);
                    String a2 = new String(tm3);
                    grid[i+1] = a2;
                    flag = 0;
                }
                else if(flag == 0 && flag1 == 1){
                    String a1 = new String(tm2);
                    //String a2 = new String(tm3);
                    grid[i-1] = a1;
                    flag1 = 0;
                }
            }
            count++;
            ans = grid;
            if((n+1)%4==0){
                //grd = grid;
                break;
            }
        }
        }
    }
    return(ans);
}

private static final Scanner scanner = new Scanner(System.in);

public static void main(String[] args) throws IOException {
    BufferedWriter bufferedWriter = new BufferedWriter(new FileWriter(System.getenv("OUTPUT_PATH")));

    String[] rcn = scanner.nextLine().split(" ");

    int r = Integer.parseInt(rcn[0]);

    int c = Integer.parseInt(rcn[1]);

    int n = Integer.parseInt(rcn[2]);

    String[] grid = new String[r];

    for (int i = 0; i < r; i++) {
        String gridItem = scanner.nextLine();
        grid[i] = gridItem;
    }

    String[] result = bomberMan(n, grid);

    for (int i = 0; i < result.length; i++) {
        bufferedWriter.write(result[i]);

        if (i != result.length - 1) {
            bufferedWriter.write("\n");
        }
    }

    bufferedWriter.newLine();

    bufferedWriter.close();

    scanner.close();
}

}

Abhiskek The pattern is like if n=1 ans = grid if n%2 == 0 than all are 0's now the headache is when it is other than above cases I. For all cases the solution for n = 3,7,11,15....(i.e. the configration of grid at n=3) is same while for n = 5,9,13.... it is same as that of initial i.e. at t=1.

II. While for the second case it is like, for n = 3,7,11,15.... the solution is still same as that of the n=3 while for n = 5,9,13.... it is different from that of t=1 or initital. But for all n E (5,9,13,17...) it is same. So for worst case you need to follow the pattern mentioned(i.e. {i,j} = 0 will affect {i+-1 and j+-1}) in question for 2 times i.e. first time to find the grid for n=3,7,11... and second time for n=5,9,13,17... !!

I am not able to figure out for what cases of n=5,9,13,17..... we have to use I and for what cases II.

Hope it will be helpful for u.