Task: Random Latin squares
C#: using System;
using System.Collections.Generic;

namespace RandomLatinSquares {
    using Matrix = List<List<int>>;

    
    static class Helper {
        private static readonly Random rng = new Random();

        public static void Shuffle<T>(this IList<T> list) {
            int n = list.Count;
            while (n > 1) {
                n--;
                int k = rng.Next(n + 1);
                T value = list[k];
                list[k] = list[n];
                list[n] = value;
            }
        }
    }

    class Program {
        static void PrintSquare(Matrix latin) {
            foreach (var row in latin) {
                Console.Write('[');

                var it = row.GetEnumerator();
                if (it.MoveNext()) {
                    Console.Write(it.Current);
                }
                while (it.MoveNext()) {
                    Console.Write(", ");
                    Console.Write(it.Current);
                }

                Console.WriteLine(']');
            }
            Console.WriteLine();
        }

        static void LatinSquare(int n) {
            if (n <= 0) {
                Console.WriteLine("[]");
                return;
            }

            var latin = new Matrix();
            for (int i = 0; i < n; i++) {
                List<int> temp = new List<int>();
                for (int j = 0; j < n; j++) {
                    temp.Add(j);
                }
                latin.Add(temp);
            }
            
            latin[0].Shuffle();

            
            for (int i = 1; i < n - 1; i++) {
                bool shuffled = false;

                while (!shuffled) {
                    latin[i].Shuffle();
                    for (int k = 0; k < i; k++) {
                        for (int j = 0; j < n; j++) {
                            if (latin[k][j] == latin[i][j]) {
                                goto shuffling;
                            }
                        }
                    }
                    shuffled = true;

                shuffling: { }
                }
            }

            
            for (int j = 0; j < n; j++) {
                List<bool> used = new List<bool>();
                for (int i = 0; i < n; i++) {
                    used.Add(false);
                }

                for (int i = 0; i < n-1; i++) {
                    used[latin[i][j]] = true;
                }
                for (int k = 0; k < n; k++) {
                    if (!used[k]) {
                        latin[n - 1][j] = k;
                        break;
                    }
                }
            }

            PrintSquare(latin);
        }

        static void Main() {
            LatinSquare(5);
            LatinSquare(5);
            LatinSquare(10); 
        }
    }
}

Java: import java.util.ArrayList;
import java.util.Collections;
import java.util.Iterator;
import java.util.List;
import java.util.Objects;

public class RandomLatinSquares {
    private static void printSquare(List<List<Integer>> latin) {
        for (List<Integer> row : latin) {
            Iterator<Integer> it = row.iterator();

            System.out.print("[");
            if (it.hasNext()) {
                Integer col = it.next();
                System.out.print(col);
            }
            while (it.hasNext()) {
                Integer col = it.next();
                System.out.print(", ");
                System.out.print(col);
            }
            System.out.println("]");
        }
        System.out.println();
    }

    private static void latinSquare(int n) {
        if (n <= 0) {
            System.out.println("[]");
            return;
        }

        List<List<Integer>> latin = new ArrayList<>(n);
        for (int i = 0; i < n; ++i) {
            List<Integer> inner = new ArrayList<>(n);
            for (int j = 0; j < n; ++j) {
                inner.add(j);
            }
            latin.add(inner);
        }
        
        Collections.shuffle(latin.get(0));

        
        for (int i = 1; i < n - 1; ++i) {
            boolean shuffled = false;
            shuffling:
            while (!shuffled) {
                Collections.shuffle(latin.get(i));
                for (int k = 0; k < i; ++k) {
                    for (int j = 0; j < n; ++j) {
                        if (Objects.equals(latin.get(k).get(j), latin.get(i).get(j))) {
                            continue shuffling;
                        }
                    }
                }
                shuffled = true;
            }
        }

        
        for (int j = 0; j < n; ++j) {
            List<Boolean> used = new ArrayList<>(n);
            for (int i = 0; i < n; ++i) {
                used.add(false);
            }
            for (int i = 0; i < n - 1; ++i) {
                used.set(latin.get(i).get(j), true);
            }
            for (int k = 0; k < n; ++k) {
                if (!used.get(k)) {
                    latin.get(n - 1).set(j, k);
                    break;
                }
            }
        }

        printSquare(latin);
    }

    public static void main(String[] args) {
        latinSquare(5);
        latinSquare(5);
        latinSquare(10);
    }
}