MathDB
Problems
Contests
Undergraduate contests
Putnam
1964 Putnam
A6
A6
Part of
1964 Putnam
Problems
(1)
Putnam 1964 A6
Source: Putnam 1964
3/5/2022
Let
S
S
S
be a finite subset of a straight line. Say that
S
S
S
has the repeated distance property if every value of the distance between two points of
S
S
S
(except the longest) occurs at least twice. Show that if
S
S
S
has the repeated distance property then the ratio of any two distances between two points of
S
S
S
is rational.
Putnam
ratio
geometry