space not occupied by walk." But Balbus expressly said that the walk "used up the whole of the area." Oh, Tympanum! My tympa is exhausted: my brain is num! I can say no more.
Hecla indulges, again and again, in that most fatal of all habits in computation—the making two mistakes which cancel each other. She takes x as the width of the garden, in yards, and x + ½ as its length, and makes her first "coil" the sum of x½, x½, x-1, x-1, i.e. 4x-3: but the fourth term should be x-1½, so that her first coil is ½ a yard too long. Her second coil is the sum of x-2½, x-2½, x-3, x-3: here the first term should be x-2 and the last x-3½: these two mistakes cancel, and this coil is therefore right. And the same thing is true of every other coil but the last, which needs an extra half-yard to reach the end of the path: and this exactly balances the mistake in the first coil. Thus the sum total of the coils comes right though the working is all wrong.
Of the seven who are right, Dinah Mite, Janet, Magpie, and Taffy make the same assumption as C. G. L. and Co. They then solve by a Quadratic. Magpie also tries it by Arithmetical Progression, but fails to notice that the first and last "coils" have special values.
Alumnus Etonæ attempts to prove what C. G. L. assumes by a particular instance, taking a garden 6 by 5½. He ought to have proved it generally: what is true of one number is not always true of