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circumstances? She begins by assuming that lemonade is 4d. a glass, and sandwiches 3d. each, (making with the 2 given equations, four conditions to be fulfilled by three miserable unknowns!). And, having (naturally) developed this into a contradiction, she then tries 5d. and 2d. with a similar result. (N.B. This process might have been carried on through the whole of the Tertiary Period, without gratifying one single Megatherium.) She then, by a "happy thought," tries half-penny biscuits, and so obtains a consistent result. This may be a good solution, viewing the problem as a conundrum: but it is not scientific. Janet identifies sandwiches with biscuits! "One sandwich + 3 biscuits" she makes equal to "4." Four what? Mayfair makes the astounding assertion that the equation, $\scriptstyle s\ +\ 3b\ =\ 3$, "is evidently only satisfied by $\scriptstyle s\ =\ {\frac {3}{2}},\ b\ =\ {\frac {1}{2}}$"! Old Cat believes that the assumption that a sandwich costs 1½d. is "the only way to avoid unmanageable fractions." But why avoid them? Is there not a certain glow of triumph in taming such a fraction? "Ladies and gentlemen, the fraction now before you is one that for years defied all efforts of a refining nature: it was, in a word, hopelessly vulgar. Treating it as a circulating decimal (the treadmill of fractions) only made matters worse. As a last resource, I reduced it to its lowest terms, and extracted its square root!" Joking