Task: Abbreviations, automatic
C#: using System;
using System.Collections.Generic;

namespace Abbreviations {
    class Program {
        static void Main(string[] args) {
            string[] lines = System.IO.File.ReadAllLines("days_of_week.txt");
            int i = 0;

            foreach (string line in lines) {
                i++;
                if (line.Length > 0) {
                    var days = line.Split();
                    if (days.Length != 7) {
                        throw new Exception("There aren't 7 days in line " + i);
                    }

                    Dictionary<string, int> temp = new Dictionary<string, int>();
                    foreach (string day in days) {
                        if (temp.ContainsKey(day)) {
                            Console.WriteLine(" ∞  {0}", line);
                            continue;
                        }
                        temp.Add(day, 1);
                    }

                    int len = 1;
                    while (true) {
                        temp.Clear();
                        foreach(string day in days) {
                            string key;
                            if (len < day.Length) {
                                key = day.Substring(0, len);
                            } else {
                                key = day;
                            }
                            if (temp.ContainsKey(key)) {
                                break;
                            }
                            temp.Add(key, 1);
                        }
                        if (temp.Count == 7) {
                            Console.WriteLine("{0,2:D}  {1}", len, line);
                            break;
                        }
                        len++;
                    }
                }
            }
        }
    }
}

Java: import java.io.IOException;
import java.nio.file.Files;
import java.nio.file.Path;
import java.nio.file.Paths;
import java.util.HashMap;
import java.util.List;
import java.util.Map;

public class Abbreviations {
    public static void main(String[] args) throws IOException {
        Path path = Paths.get("days_of_week.txt");
        List<String> readAllLines = Files.readAllLines(path);
        for (int i = 0; i < readAllLines.size(); i++) {
            String line = readAllLines.get(i);
            if (line.length() == 0) continue;

            String[] days = line.split(" ");
            if (days.length != 7) throw new RuntimeException("There aren't 7 days on line " + (i + 1));

            Map<String, Integer> temp = new HashMap<>();
            for (String day : days) {
                Integer count = temp.getOrDefault(day, 0);
                temp.put(day, count + 1);
            }
            if (temp.size() < 7) {
                System.out.print(" ∞  ");
                System.out.println(line);
                continue;
            }

            int len = 1;
            while (true) {
                temp.clear();
                for (String day : days) {
                    String sd;
                    if (len >= day.length()) {
                        sd = day;
                    } else {
                        sd = day.substring(0, len);
                    }
                    Integer count = temp.getOrDefault(sd, 0);
                    temp.put(sd, count + 1);
                }
                if (temp.size() == 7) {
                    System.out.printf("%2d  %s\n", len, line);
                    break;
                }
                len++;
            }
        }
    }
}