EXCEL COUNT OR SUM IF WITH DUPLICATES PROBLEM??

I have an issue that I don't know is possible to do without doing it by hand.  Please open the excel file before proceeding.

I have a list of parts that are classified by component.  The fields BXZ,ROAD,STUNT,CRUISER are boolean not actual part counts.  They are 1 if that part is needed for that component for that model or 0 if not.  Some parts are multiuse.

To the right I have a "complexity matrix".  I can use sumif and count if to get total part complexity and permodel complexity.  the problem comes when I need to bucket to models together.  I can not just add them because of the common parts.  I have included the correct answer just by counting them and typing it in myself.

What I need is a forumula/method for figuring cells q3 and r3 out correctly without doing it by hand.

Any thoughts?
ComplexityExample.xlsx
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drhamel69Asked:
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Rory ArchibaldCommented:
Should it be 5 rather than 4 for WHEEL for BMX & STUNT?
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Rory ArchibaldCommented:
If so, then:
=SUMPRODUCT(($A$3:$A$14=J3)*((D3:D14+F3:F14)>0))
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drhamel69Author Commented:
I am sorry you are correct.  The other thing I forgot to put is it needs to be vlookup style.  I mean I will have a list of 100 components of varying part numbers.  So I can't reference cells directly.
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Rory ArchibaldCommented:
I'm not sure what you mean by "vlookup style". Can you clarify?
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ragnarok89Commented:
Wouldn't the answer be 5 for BMX and Stunt? 234,4561,53113,5463, and 2323 are 5 parts...

Assuming I am correct:

=SUM((D3:D8&F3:F8="10")*1)+SUM((D3:D8&F3:F8="01")*1)+SUM((D3:D8&F3:F8="11")*1)

This is an array formula, so press Ctrl-Shift-Enter when you finish typing it.
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drhamel69Author Commented:
This actually works but can you explain how?  Sorry but it has just driven me nuts.
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drhamel69Author Commented:
I am sorry I mean rorya's works.
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Rory ArchibaldCommented:
It checks if each item in col A matches J3 (WHEEL) and returns either True or False.
It then checks if adding up the values in col D and F is more than 0 and returns True or False
These two arrays of True/False values are then multiplied together (in Excel, TRUE=1, FALSE=0) to give a final array of 1s and 0s and then adds these up.
Does that make sense?
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