Mine

import java.util.ArrayDeque;
import java.util.Deque;


public class Foo {
	private final static double[] nums =
        {
                40.58,
                49.50,
                51.50,
                71.90,
                76.80,
                85.00,
                94.90,
                95.40,
                105.40,
                116.95,
                131.50,
                144.40,
                149.11,
                155.39,
                168.15,
                175.50,
                234.20,
                269.76,
                280.19,
                643.00,
        };
       
        private final static double result = 1084.83;
        private static Deque<Integer> numbers=new ArrayDeque<>();
        
        public static void main(String[] args) {
			double value=result;
			int i=nums.length-1;
			while(true){
				value=value-nums[i];
				if(value<-0.005){
					value=value+nums[i];
				}else if(value<0.005){
					numbers.push(i);
					break;
				}else{
					numbers.push(i);
				}
				i--;
				while(i<0){
					i=numbers.pop();
					value=value+nums[i];
					i--;
				}
			}
			System.out.println("Solution:");
			for(int number: numbers){
				System.out.println(nums[number]);
			}
		}
}