Google Spreadsheet: SUMIFS for same Column - google-sheets

I've got a problem in Google Spreadsheets:
I don't know why, but for Google there is a problem to use the SUMIFS formula.
When I try to use the SUMIFS formula for different criteria, for the same column, the output is always zero 0.
I tried aleady other things, but anyways it doesn't work.
Here are my examples:
Example 1
=SUMMIFS('Sheet1'!G1:G100;'Sheet1'!C1:C100;"Criteria1";'Sheet1!C1:C100;"Criteria2";'Sheet1'!D1:D100;"Criteria3")
Example 2
=SUMMIFS('Sheet1'!G1:G100;'Sheet1'!C1:C100;{"Criteria1" ;"Criteria2"};'Sheet1'!D1:D100;"Criteria3")
Example 3
=SUMMIFS('Sheet1'!G1:G100;'Sheet1'!C1:C100;"*Criteria1"&"Criteria2";Sheet1'!D1:D100;"Criteria3")
Non of these work. I dont know what I should do. Anyone has an idea?
Thanks in Advance

This behavior is probably correct. SUMIF criteria are connected AND not OR. This means all criteria need to be true.
So if you have two criteria on the same column it is very likely that only one of them can be true at the same time. Eg. column C can not be "Car" and "Book" at the same time. Therefore it is never count into the sum and always results 0.
To OR connect criteria have a look here: SUMIFS with OR.

this formula works:
=SUM(ARRAYFORMULA(SUMIF('Sheet1'!G1:G100;'Sheet1'!C1:C100 & 'Sheet1'!C1:C100 ;{"Criteria1";"Criteria2"} ; 'Sheet1'!D1:D100;"Criteria3")))
Anyways the bad thing is, that this formula cant disting date criterias.
Example1:
=SUMIFS(G2:G100;D2:D100;">=01.06.2011";F2:F100;"<=30.07.2011")
Does work, but this example 2 doesnt work:
Example 2:
=SUM(ARRAYFORMULA(SUMIF(D2:D100 & F2:F100;">=01.06.2011"&"<=30.07.2011";G2:G100)))
I Dont know why it doesnt work, has anybody a solution for this ?
Thanks in advance.

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I probably did not phrase my question accurately. Is there a way to remove the result 'a' because it fulfils the '<>1' condition? I am pretty sure a mixture of query and arrayformula is needed but I can't figure it out.
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How would I go about formatting an arrayformula for this?:
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=$D10*(sum($F10:$I10))
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UPDATE************************************************************************
I've just figured out that =arrayformula(D7:D*(F7:F+G7:G+H7:H+I7:I)) works but I might need to add and subtract columns too. Is there a way to make it work with sum()?
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The best way to solve math problem is to split it.
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=ArraFormula(D10:D1000)
And the hard part is to make ArrayFormula with sum. This part was already asked and answered here by AdamL. In your case:
=ArrayFormula(SUMIF(IF(COLUMN(F1:I1),ROW(A10:A1000)),ROW(A10:A1000),F10:I1000))
And your final formula is
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I'm trying to summarize data from several Google spreadsheet' sheets in a single one but I have some issues with SUMIF and FIND.
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I don't know why the above SUMIF doesn't work, what I've tested and works is:
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