Here is a wooden disc, about an inch thick, that has been sitting for over a hundred years on the counter in a little country store in Vermont. The circumference of the disc is exactly 27 in. (the diameter is a little less than 9 in.). There are six wooden pegs sticking out of the edge of the disc; two of them are shown. The disc is used to measure lengths of ribbon. The pegs are arranged so that any unit length of ribbon, from 1 to 27 inches, can be measured simply by laying off the ribbon along the edge of the disc between some pair of nails or other. Where can you put the other four pegs so that this is possible?
Source: More Math Teasers (1973)