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Default 3d References

If I have a number of worksheets between a worksheet called FIRST and a
worksheet called LAST in a workbook I can sum the contents of cells, say A1,
on all these worksheets with =SUM(FIRST:LAST!A1). The sum will, of course,
include the contents of FIRST!A1 and LAST!A1. If, however, there is some
condition that determines which cells to include in the sum, say the contents
of cell B1=1, on each worksheet I can't use
=SUMIF(FIRST:LAST!B1,"=1",FIRST:LAST!A1). I get a #VALUE! error.

Question 1. Why can't I use a 3d reference with SUMIF?
Question 2. Any ideas about how to solve this problem?
 
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