Hello 1819,
This macro should work for you. I have tested it on the workbook you posted. It starts at cell "A1" and determines the table rows and columns automatically.
All duplicates are removed in the row and the cells remain contiguous. Only the cell values are changed. The formatting for each cell remains unchanged.
Sub DeleteDupsInRows()
Dim DataRow As Variant
Dim Dict As Object
Dim j As Long
Dim k As Long
Dim Key As String
Dim lastCol As Long
Dim lastRow As Long
Dim Rng As Range
Dim Wks As Worksheet
Set Wks = ActiveSheet
Set Rng = Wks.Range("A1")
lastCol = Wks.Cells.Find("*", , xlValues, xlWhole, xlByColumns, xlPrevious, False, False, False).Column
lastRow = Wks.Cells.Find("*", , xlValues, xlWhole, xlByRows, xlPrevious, False, False, False).Row
If lastRow < Rng.Row Then Exit Sub
Set Rng = Rng.Resize(lastRow - Rng.Row + 1, lastCol - Rng.Column + 1)
Set Dict = CreateObject("Scripting.Dictionary")
Dict.CompareMode = vbTextCompare
For j = 1 To Rng.Rows.Count
DataRow = Rng.Rows(j).Value
For k = 1 To UBound(DataRow, 2)
Key = Trim(DataRow(1, k))
If Key <> "" Then
If Not Dict.Exists(Key) Then
Dict.Add Key, 1
End If
End If
Next k
Rng.Rows(j).Value = Empty
Rng.Rows(j).Resize(1, Dict.Count).Value = Dict.Keys
Dict.RemoveAll
Next j
End Sub