Problem #2
This month's problem was contributed by Philippe Fondanaiche of Paris,
France:
Find the largest integer n such that n real numbers
x1, x2, ..., xn can
be chosen in the interval [0,1] such that
- x1 and x2 are in different halves
of the interval,
- x1, x2, and x3
are in different thirds of the interval,
.
.
.
- x1, ..., xn are in different
nths of the interval.
Note: By "halves" we mean the intervals [0,1/2] and [1/2,1]. By "thirds"
we mean the intervals [0,1/3], [1/3,2/3], and [2/3,1]. Etc.
Give an explicit example of x1, x2,
..., xn for the maximum possible n.