Sam Loyd and Mrs. Perkins's Quilt

Sam Loyd produced this puzzle a while back, and it has become one his most famous puzzles:

"For Christmas, Mrs. Potipher Perkins received a very pretty patchwork quilt constructed of 169 square pieces of silk material. The puzzle is to find the smallest number of square portions of which the quilt could be composed and show how they might be joined together. Or, to put it the reverse way, divide the quilt into as few square portions as possible by merely cutting the stitches."

Warning: The diagram above shows a 14 x 14 square quilt that has more than 169 square pieces.  The diagram is wrong.  What is the smallest number of square pieces that this quilt can be composed of?

The solution will be posted on Saturday.

David