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Default sumif for a specific number of cells

I have a 52 columns, one for each week of the year. Each column has 10 rows
of data. I need a totals line which, for each row, sums 13 columns (13 weeks)
but the 13 colums it sums needs to be changable ie sum weeks 1-13 or 14-27 or
32-35 etc. Any idea how I make this formula driven - my thoughts were to use
a sumif formula and input the criteria to sum the numbers between week 14 and
27 (taking 14 and 27 from an input in another cell).

Any ideas on how I solve this? Thanks. Simon
 
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