= Solution
\b[<Gallstones> contain chiefly <cholesterol> and/or <bile pigment>, with variable <calcium salts> and an organic matrix.] They are mixtures with different predominant components, not one compound with a universal formula. The period word <cholesterol>[cholesterin] denotes <cholesterol>.
Cholesterol-rich stones contain crystalline <cholesterol>, often with a smaller pigmented nucleus and layers of other material. Mixed stones combine <cholesterol>, pigment, <calcium salts> and an organic matrix including <mucin>. Pigment stones contain much less <cholesterol>; a major constituent is <calcium bilirubinate>, related to the <bile pigment> <bilirubin>. Minor inorganic constituents can include <calcium carbonate> and <calcium phosphate>. Not every visibly dark stone has the same composition, and no fixed percentage follows from the question.<Gallstone Composition by Merck Manual Professional Edition>[Cholelithiasis: cholesterol, black pigment and brown pigment stone composition]{ref}
The useful modern subdivision of pigment stones is into black and brown types. Black stones commonly contain polymerised pigment with <calcium salts>; brown stones include <calcium bilirubinate> and calcium salts of fatty acids, particularly in infected stagnant duct bile. These refinements explain why neither “all stones are <cholesterol>” nor “all stones are lime salts” is adequate.<Gallstones by NIDDK>[Definition and facts; symptoms and causes: cholesterol, bilirubin and bile composition]{ref}
Chemical examination should distinguish the fractions rather than infer them merely from the external colour. <Cholesterol> can be extracted with a suitable organic solvent and recognised in recrystallised material; microscopy can show characteristic plate-like crystals. A mineral residue after removal or destruction of organic matter indicates an inorganic fraction, but residue alone cannot identify a particular salt. Layering, facets and colour describe growth and packing and are not chemical analyses. In particular, <calcium bilirubinate> is not interchangeable with <calcium carbonate>, and <cholesterol> is not a <bile salt>.
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