its _separate_ value. The other competitor, who is
wrong throughout, is either J. M. C. or T. M. C.: but, whether he be a
Juvenile Mis-Calculator or a True Mathematician Confused, he makes the
answers 7_d._ and 1_s._ 5_d._ He assumes, with Too Much Confidence, that
biscuits were 1/2_d._ each, and that Clara paid for 8, though she only
ate 7!

We will now consider the 13 whose working is wrong, though the answer is
right: and, not to measure their demerits too exactly, I will take them
in alphabetical order. ANITA finds (rightly) that "1 sandwich and 3
biscuits cost 3_d._," and proceeds "therefore 1 sandwich = 1-1/2_d._, 3
biscuits = 1-1/2_d._, 1 lemonade = 6_d._" DINAH MITE begins like ANITA:
and thence proves (rightly) that a biscuit costs less than a 1_d._:
whence she concludes (wrongly) that it _must_ cost 1/2_d._ F. C. W. is
so beautifully resigned to the certainty of a verdict of "guilty," that
I have hardly the heart to utter the word, without adding a "recommended
to mercy owing to extenuating circumstances." But really, you know,
where _are_ the extenuating circumstances? She begins by assuming that
lemonade is 4_d._ a glass, and sandwiches 3_d._ 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 5_d._ and 2_d._ 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, _s_ + 3_b_ = 3, "is
evidently only satisfied by _s_ = 3/2, _b_ = 1/2"! OLD CAT believes that
the assumption that a sandwich costs 1-1/2_d._ 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