A type of Ruler considered by Guy (1994) which has distinct marks spaced such that the distances between marks can be used to measure all the distances 1, 2, 3, 4, ... up to some maximum distance . Such a ruler can be constructed from a Perfect Difference Set by subtracting one from each element. For example, the Perfect Difference Set gives 0, 1, 4, 6, which can be used to measure , , , , , (so we get 6 distances with only four marks).

**References**

Guy, R. K. ``Modular Difference Sets and Error Correcting Codes.'' §C10 in
*Unsolved Problems in Number Theory, 2nd ed.* New York: Springer-Verlag, pp. 118-121, 1994.

© 1996-9

1999-05-26