This month's problem was contributed by Philippe Fondanaiche of Paris, France:

Find the largest integer *n* such that *n* real numbers
*x*_{1}, *x*_{2}, ..., *x*_{n} can
be chosen in the interval [0,1] such that

*x*_{1}and*x*_{2}are in different halves of the interval,*x*_{1},*x*_{2}, and*x*_{3}are in different thirds of the interval,

.

.

.

*x*_{1}, ...,*x*_{n}are in different*n*^{th}s of the interval.

Give an explicit example of *x*_{1}, *x*_{2},
..., *x*_{n} for the maximum possible *n*.