Fred: Pls email me these pix and I'll host them. --rwg I cannot refrain from adding: Screw DropBox. << Scale diagrams of these solutions might be appreciated here ...? >> Quite so. In a pleasant inversion of the scholastic dictum that a diagram does not constitute a proof, a clutch of accurate diagrams immediately discloses that: The obvious interpretation of a signed sightline distance --- that the correct angle is made only with a line segment directed _away_ from the tower --- was after all perfectly correct. Hence --- assuming an observer lacking eyes in the back of the head --- my second and fourth solutions were duds, and only the other two remain standing (outside the rectangle). Corrected summary & diagrams, and program & results, are posted at https://www.dropbox.com/s/gva6w9ni9y6svp1/battersea.pdf https://www.dropbox.com/s/175plix3vkvxqoj/battersea_run.txt This has turned out to be an unexpectedly involved exercise: in particular, a neat elementary application of Gröbner bases, as well as an excellent topic for an undergraduate project; perhaps in a situation calling for an especially --- ahem --- challenging one ... Fred Lunnon