Selected Answer
Destiny
The answer from Variatus is neat and perhaps your best option. This answer works too and might help you understand the tutorial better (or the part I looked at)...
If you look at my version of your file (attached), try using Format Painter to copy the colour of a green cell (K4) to Z10 say then type a number in Z10 (or copy K4 to 10). The Vacations total cell AM10 will change to suit. Works for your other colours or date cells, provided the correct colour is in the cell with a number..
That's because I've added a simple macro (using a named range) and created the appropriate SUMIF formula. To understand that, see below...
In your *.xlsx file, sample cell AM4 formula is =SUMIFS(B4:AL4,AM28:AM30,65280) which means sum the numbers in B4:AL4 if a corresponding cell in AM28:AM30 is ? (you put 65280 for the colour green rather than = 65280) but even that doesn't work.
The tutorial Sumifs formula relied on a cell next to the summed cell contain a number representing the colour. In my file, I've added (hidden) below the month rows (e.g. hidden row 5 holds the colours for individual date hours cells in row 4 January).
This macro in the file senses when a number is changed in any hours cells then puts the cell colour value in the hidden cell below - note that the Offset is 1,0 i.e. 1 row down, 0 columns across (rather than 0,1 for one column right in the tutorial):
Private Sub Worksheet_Change(ByVal Target As Range)
If Not Intersect(Target, ActiveSheet.Range("DayColors")) Is Nothing Then
For Each jCell In Target
jCell.Offset(1, 0).Value = jCell.Interior.Color
Next jCell
End If
End Sub
REVISION 1: The code above (and attached file) are changed so it works if you copy/paste of several cells at once. The For Each...Next loop does the colour value calculation for how ever many cells are copy/pasted in the hours row.
The code is simple because I've used Name Manager (under the Formulas ribbon) to define a named range called "DayColors" as the hours cells in B4:AL4 plus B8:AL8 etc.
Now it's easy to create the formula to add those values. E.g. the January vacations total is:
=SUMIF(B5:AL5,"=65280",B4:AL4)
It's a SUMIF (not SUMIFS) since there only one criteria and means if a value in (hidden) cells B5:AL5 equals 65280 (the colour value added by the macro) then add the corresponding value in the row above B4:AL4 to the sum.
I leave you to see how the same is done for Sick and Personal time (already done in my file).
That's it!