Simplest Solution I have Seen So far:-

Code

class Result {

public static String ans="";

public static boolean Solve(List<Integer>arr,int prev,String cur,int idx,boolean map[]  []){
        prev=prev%101;

 if(idx==arr.size()){
        if(prev%101==0){
                 ans=cur;
                    return true;  
             }
return false;
}

 //Checking if at this index Previsiously we Got this remainder(prev)

if(map[idx][prev+101])return false;
map[idx][prev+101]=true;

    //recursion   

    if(Solve(arr,prev+arr.get(idx)%101,cur+"+"+arr.get(idx),idx+1,map))return true;
    if(Solve(arr,prev-arr.get(idx)%101,cur+"-"+arr.get(idx),idx+1,map))return true;
    if(Solve(arr,prev*arr.get(idx)%101,cur+"*"+arr.get(idx),idx+1,map))return true;

   return false;
}

public static String arithmeticExpressions(List<Integer> arr){

boolean[][]map=new boolean[arr.size()][2*101];

Solve(arr,arr.get(0),""+arr.get(0),1,map);

 return ans;
}

}