Problem #206 says:

Find the unique positive integer whose square has the form 1_2_3_4_5_6_7_8_9_0,
where each “_” is a single digit.

The range of number to check can be narrowed down with a calculator and some common sense. Then its just a square and check procedure. Solution is in c# and requires the .Net 4.0 framework for its parallel extensions.

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Linq.Parallel;
using System.Threading;
using System.Threading.Tasks;
using System.Diagnostics;
using System.Numerics;
using System.Text.RegularExpressions;

namespace Net4Test
{
    class Program
    {
        static object LockHandle = new object();
        static long Answer = 0;
        static void Main(string[] args)
        {
            Stopwatch sw = new Stopwatch();
            sw.Start();
            Regex Test = new Regex(
            "[1][0-9][2][0-9][3][0-9][4][0-9]" +
            "[5][0-9][6][0-9][7][0-9][8][0-9][9][0-9][0]");

            Parallel.For(1360000000, 1390000000, i =>
                {

                    BigInteger biI = i;

                    if (Test.IsMatch((biI * biI).ToString()))
                    {
                        Answer = i;
                    }
                });

            Console.WriteLine(Answer);
            sw.Stop();
            Console.WriteLine(sw.Elapsed);
            Console.ReadLine();
        }

    }
}