Task: Nonoblock
C#: using System;
using System.Linq;
using System.Text;

public static class Nonoblock
{
    public static void Main() {
        Positions(5, 2,1);
        Positions(5);
        Positions(10, 8);
        Positions(15, 2,3,2,3);
        Positions(5, 2,3);
    }

    public static void Positions(int cells, params int[] blocks) {
        if (cells < 0 || blocks == null || blocks.Any(b => b < 1)) throw new ArgumentOutOfRangeException();
        Console.WriteLine($"{cells} cells with [{string.Join(", ", blocks)}]");
        if (blocks.Sum() + blocks.Length - 1 > cells) {
            Console.WriteLine("No solution");
            return;
        }
        var spaces = new int[blocks.Length + 1];
        int total = -1;
        for (int i = 0; i < blocks.Length; i++) {
            total += blocks[i] + 1;
            spaces[i+1] = total;
        }
        spaces[spaces.Length - 1] = cells - 1;
        var sb = new StringBuilder(string.Join(".", blocks.Select(b => new string('#', b))).PadRight(cells, '.'));
        Iterate(sb, spaces, spaces.Length - 1, 0);
        Console.WriteLine();
    }

    private static void Iterate(StringBuilder output, int[] spaces, int index, int offset) {
        Console.WriteLine(output.ToString());
        if (index <= 0) return;
        int count = 0;
        while (output[spaces[index] - offset] != '#') {
            count++;
            output.Remove(spaces[index], 1);
            output.Insert(spaces[index-1], '.');
            spaces[index-1]++;
            Iterate(output, spaces, index - 1, 1);
        }
        if (offset == 0) return;
        spaces[index-1] -= count;
        output.Remove(spaces[index-1], count);
        output.Insert(spaces[index] - count, ".", count);
    }

}

Java: import java.util.*;
import static java.util.Arrays.stream;
import static java.util.stream.Collectors.toList;

public class Nonoblock {

    public static void main(String[] args) {
        printBlock("21", 5);
        printBlock("", 5);
        printBlock("8", 10);
        printBlock("2323", 15);
        printBlock("23", 5);
    }

    static void printBlock(String data, int len) {
        int sumChars = data.chars().map(c -> Character.digit(c, 10)).sum();
        String[] a = data.split("");

        System.out.printf("%nblocks %s, cells %s%n", Arrays.toString(a), len);
        if (len - sumChars <= 0) {
            System.out.println("No solution");
            return;
        }

        List<String> prep = stream(a).filter(x -> !"".equals(x))
                .map(x -> repeat(Character.digit(x.charAt(0), 10), "1"))
                .collect(toList());

        for (String r : genSequence(prep, len - sumChars + 1))
            System.out.println(r.substring(1));
    }

    
    static List<String> genSequence(List<String> ones, int numZeros) {
        if (ones.isEmpty())
            return Arrays.asList(repeat(numZeros, "0"));

        List<String> result = new ArrayList<>();
        for (int x = 1; x < numZeros - ones.size() + 2; x++) {
            List<String> skipOne = ones.stream().skip(1).collect(toList());
            for (String tail : genSequence(skipOne, numZeros - x))
                result.add(repeat(x, "0") + ones.get(0) + tail);
        }
        return result;
    }

    static String repeat(int n, String s) {
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < n; i++)
            sb.append(s);
        return sb.toString();
    }
}