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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?

Jun 5, 2019

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This is similar to the "toothpick" problem.....imagine each perforation  to be a toothpick

The number of perforations =

(number of stamps in each row)*(3 -1)rows + (number of stamps in each column)*(3-1)columns  =

( 3)(2)  + (3)(2)  =  6 + 6 =   12 perforations

So....each perforation   =    18/12 =  1.5 inches

Using similar reasoning.....the number of perforations on a 6x6 sheet  =

(6)(6 - 1) + 6(6-1)  =  (6)(5) + (6)(5)  =  30 + 30  =  60

So...the total length of the creases on a 6x6 sheet  =  60 * 1.5  =  90 inches   Jun 5, 2019
edited by CPhill  Jun 5, 2019