List all the sheetnames to search within in a single column of your summary sheet. Then name that range, through Insert|Name|Define and call it: TabNames
Then use formula:
=SUMPRODUCT(SUMIF(INDIRECT("'"&TabNames&"'!A1:A10"),A1,INDIRECT("'"&TabNames&"'!C1:C10")))
adjust ranges to suit.
Note: If your sheets are truly named in some sort of sequential manner, like Sheet2, Sheet3, Sheet4, etc... then you don't need to list the sheetnames, you can use something more like:
=SUMPRODUCT(SUMIF(INDIRECT("'Sheet"&ROW(INDIRECT("2:10"))&"'!A1:A10"),A1,INDIRECT("'Sheet"&ROW(INDIRECT("2:10"))&"'!C1:C10")))
Adjust ranges to suit..where 2:10 means Sheet2:Sheet10.
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