A perfect ruler is a Golomb ruler whose marks measure each integer distance from
1 through its length exactly once. For example, the marks
0, 1, 4, 6 measure 
,
, 
, 
, 
, and 
, giving six distances using
four marks, as illustrated above (Gardner 1983, Fig. 91, and pp. 153-154).
Subtracting the least mark from every mark normalizes a Golomb ruler to start at 0 without changing any differences. A perfect difference set uses differences modulo an integer; it does not in general give a perfect ruler when its representatives are treated as ordinary marks.
No perfect Golomb ruler, i.e., a ruler that uniquely measures distances up to its length, exists for five or more marks (Golomb 1972; Gardner 1983, p. 154).
