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# help

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Pat has two sheets of large, square stamps. One sheet consists of 9 stamps arranged in a 3-by-3 square. (That's 3 stamps by 3 stamps, not 3 inches by 3 inches.) The other sheet consists of 36 stamps arranged in a 6-by-6 square. The stamps on each sheet are separated by perforated creases. All the stamps on both sheets are the same shape and size.

The total length of the creases on the 3-by-3 sheet is 18 inches.

How many inches of creases does the 6-by-6 sheet have?

Jan 19, 2018

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The number of creases separating the stamps on  a sheet of  n  stamps  is given by

(2n - 1) ( n - 1) + (n -1)   =

(n - 1) (2n - 1 + 1) =

(n - 1) (2n)

So.....for   3 stamps, we have that  that the length of each perforated crease is

18/ [ (n - 1)(2n) ]  =  18 / [ (2)(6)]  =  18 / 12   =   1.5 inches each

And the number of  perforated creases separating the stamp on a 6 X 6  sheet   =

(6 - 1)(2 * 6)  =  5 * 12  =  60

So....the total length of the creases  =  60 * 1.5   =  90  inches   Jan 19, 2018