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?
+128474 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
