The imperforate edges on 2 or 3 sides made the blocks easily identifiable as coming from a booklet pane. In case you are not familiar with stamp booklets, here are some pictures from the internet.



Since you said they were Perf 11, that narrowed it down to 499e. There are a number of other Perf 11 2-cent Washingtons, but none of the other Perf 11's were issued in booklet form, only as sheets of 100.
The Scott Specialized catalog has a good section of information about how booklet panes were printed, including the plate layout for the 360-stamp sheets that were printed of this issue before cutting them down into booklet panes of 6.