Q:

Why does IList<>.Reverse() not work like List<>().Reverse

I have problem with List<T>.Reverse() and Reverse(this IEnumerable<TSource> source).
Look to the code:
  // Part 1
  List<int> list = new List<int> { 1, 2, 3 };

  foreach (int x in list)
    Console.Write(x);

  Console.WriteLine();

  list.Reverse();

  foreach (int x in list)
    Console.Write(x);

  Console.WriteLine();
  list.Reverse();

  // Part2
  IList<int> ilist = list;

  foreach (int x in list)
    Console.Write(x);      

  Console.WriteLine();

  ilist.Reverse();

  foreach (int x in ilist)
    Console.Write(x);

  Console.WriteLine();

  ilist.Reverse();

My result:
123
321
123
123

because Reverse()-Part1 is List<T>.Reverse(), Reverse()-Part2 is Reverse(this IEnumerable<TSource> source)
I want execute List<int>.Reverse() in Part2 for IList<int>. How I can do it?

A:

IList<int> doesn't have a Reverse method, so it uses the extension method.  The only way to use List<T>.Reverse on your IList<int> reference is to cast or convert it to a List<int>.  Casting will only work if you're sure that it's really a List<int> in the first place:
IList<int> abstractList;
var concreteList = (List<int>)abstractList;
concreteList.Reverse();

Another option would be to create a List<int> from your IList<int> instance, rather than assuming it already is a List<int>:
IList<int> abstractList;
var concreteList = new List<int>(abstractList);
concreteList.Reverse();

The reason that the Reverse extension method doesn't actually affect the underlying list is because it operates on IEnumerable<T>, which isn't necessarily writeable (none of the Enumerable extension methods make changes to the original collection, they return a new collection).
To use this version of Reverse, just use the product of the Reverse call, rather than the original list:
IList<int> abstractList;
IEnumerable<int> reversedList = abstractList.Reverse();

A:

In the second example, you're using an extension method against IEnumerable<T>, and this is not mutating the original collection but rather producing a query that would result in a sequence of your original list in reverse order. That is to say, if you want to utilize the results of ilist.Reverse(), you would say 
var reversedList = iList.Reverse(); 
// reversedList is IEnumerable<int>
// 'list' and 'ilist' are not changed

foreach (int item in reversedList)
    Console.Write(item);

