JPropp> What's the optimum amount of water to put in a jar if you want to clean the jar by putting some water in it and shaking it for a bit? I grant that the problem is ill-posed in all kinds of ways, but maybe some not-too-farfetched model gives results in line with experimental data conducted on jars of ordinary shape containing food residues of an ordinary kind. I seem to recall that number theorist David Solomon, back when we were housemates in Berkeley in the 1980s, came up with an idealization of the problem for which the optimum volume of water was 1/e times the volume of the jar. I'll ask him if he remembers any details. Jim Propp -- If, as in my note to Randi, you plan to brew tea in a jar sold full of sauerkraut, it's not clear that the answer is finite. --rwg (The problem is impregnation of the rubbery film of sealant inside the lid. Simmering several hours in Clorox helped, but insufficiently. And the human nose is pathetic compared to a bloodhound's. Or a gila monster's egg sense.)