What problem about planetary motion did Edmond Halley discuss with Robert Hooke and Christopher Wren?

Edmond Halley, Robert Hooke, and Sir Christopher Wren were engaged in a competitive effort to find a mechanical explanation for planetary motion. The specific problem they sought to solve was determining what forces would keep a planet in forward motion around the Sun without the planet either flying off into space or falling into the Sun.1

While Halley and Hooke had correctly reasoned that the force maintaining a planet's orbit must decrease as the inverse square of its distance from the Sun, they were unable to mathematically deduce a theoretical orbit that matched observed planetary motions. This challenge, which even included a prize offered by Wren, ultimately led Halley to visit Isaac Newton, who confirmed he had already solved the problem by proving that such an orbit would be an ellipse.1