  Initially stated in terms of Beatty sequences, the Fraenkel conjecture can be
reformulated as follows: for a $k$-letter alphabet A, with a fixed $k \geq 3$,
there exists a unique balanced infinite word, up to letter permutations and
shifts, that has mutually distinct letter frequencies. Motivated by the
Fraenkel conjecture, we study in this paper whether two Christoffel words can
be superimposed. Following from previous works on this conjecture using Beatty
sequences, we give a necessary and sufficient condition for the superimposition
of two Christoffel words having same length, and more generally, of two
arbitrary Christoffel words. Moreover, for any two superimposable Christoffel
words, we give the number of different possible superimpositions and we prove
that there exists a superimposition that works for any two superimposable
Christoffel words. Finally, some new properties of Christoffel words are
obtained as well as a geometric proof of a classic result concerning the money
problem, using Christoffel words.
