Something along the lines of this should do it.
Hopefully you can follow the commenting.
Code:
Sub CombineJimmysSheets()
Dim i As Integer, sht As Worksheet, RngLR As Long
Application.ScreenUpdating = False
'loop thru numbers
For i = 1 To 30
'loop thru sheets
For Each sht In ThisWorkbook.Sheets
'if sheet name found
If sht.Name = "A" & Format(i, "00") Then
With sht
'determine last row of range
RngLR = .Range("A4").End(xlDown).Row
'copy the range and paste to sheet 1
.Range("A5:P" & RngLR).Copy _
Sheets("Sheet1").Range("A" & Rows.Count).End(xlUp).Offset(1)
End With
'don't loop any further looking for sheet already found
Exit For
End If
'check next sheet
Next sht
'check for next number
Next i
Application.ScreenUpdating = True
End Sub