Try this one liner:
var o = beatles
.OrderBy( x => x.id )
.GroupBy( x => x.inst )
.Select( group => new { Group = group, Count = group.Count() } )
.SelectMany( groupWithCount =>
groupWithCount.Group.Select( b => b)
.Zip(
Enumerable.Range( 1, groupWithCount.Count ),
( j, i ) => new { j.inst, j.name, RowNumber = i }
)
);
foreach (var i in o)
{
Console.WriteLine( "{0} {1} {2}", i.inst, i.name, i.RowNumber );
}
Output:
Guitar John 1
Guitar George 2
Guitar Paul 3
drums Ringo 1
drums Pete 2