Once more with the Maiden in New Logic/Math Puzzles Posted October 8, 2019 · Edited October 8, 2019 by plasmid Added a 1/M term to account for the change in angular velocity depending on distance from the center · Report reply After more thought: Spoiler My previous answer talked about finding a circle where the maiden could have a faster radial velocity than the ogre. She would get in as good of a position as possible within that circle and then make a straight dash for the exit. Now I think her best trajectory is not a straight dash, but one that bends away from the ogre’s current position a little. If M is the maiden's distance from the center of the lake and dM is the rate of change in M, and dA is the rate of change in the angle from the ogre to the center of the lake to the maiden, then the optimal path should be the one with the largest dM/dA ratio. Define angle B as the difference between the direction the maiden is traveling and a line straight out from the center. dM is f cos(B). dA is the ogre’s angular velocity minus the maiden’s angular velocity, so 1 – f sin(B)/M. In principle you could find the angle B that maximizes dM/dA = f cos(B) / (1 – f sin(B)/M) by setting the derivative with respect to B to zero. But that would tell you the best strategy if she can change direction instantaneously and I’m not yet sure how to incorporate her turning speed into that part of the answer.