+1443 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?
+129852 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
