The French mathematician Vercingetorix solved this problem just before Julius Caesar invaded Gaul.
Menage’ a trois
Whereby one body (A) of the 3 bodies can only occupy one
body (B) at the same time the third body (C) is orbiting
the second body (B) ...Re-entry may be facilitated by
body (A) only if body (B) and body (C) remain
in synchronous orbits. Asynchronicity may occur at any
time body (A) separates from body (B) and enters the
gravitational field of body (C), thus causing immediate
collision of bodies (A) and (C). Such collisions may result
in spawning of new bodies, though only 1/4 mass of one of
the bodies (A), (B), or (C).
Frankly, there were no French in Julius Caesar’s time, just Bois and Gauls.................
The web can show us many images of three bodies solving a particular problem, even when the initial conditions are unknown.