Not sure I get the rationality aspect of this—seems like a pretty basic high-school geometry problem. The guard is stationary on a line, and his visibility is a semi-circle. The line from the guard to you is perpendicular to the wall, so you can go a quarter-circle in either direction. Circumference is 2*Pi*r, so a quarter is 1⁄2 * Pi * r. And you’ll cross the wall at the same distance from the guard you start at, r. Well, r plus epsilon (for both calculations), I guess, but that rounds to r for this calculation.That’s not the answer you give, so maybe I don’t understand something. Or maybe it’s a formatting error.
(It was my first time trying tags, I had the problem set tag in mind. I also intended for it to be a timed test, but realized that it might be to on the nose. )
It is a formatting error though and I’ve had to go back and edit a couple times to understand where I should make discrepancies in the text so that things aren’t left open ended. In certain cases defining certain aspects has changed the answer, but now I know the specificity needed for these types of exercises.