Page:Carroll - Tangled Tale.djvu/156

140 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,, and make the same assumption as C. G. L. and. They then solve by a Quadratic. also tries it by Arithmetical Progression, but fails to notice that the first and last "coils" have special values.

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 others. solves it by an Arithmetical Progression. It is right, but too lengthy to be worth as much as a Quadratic.

proves it very neatly, by pointing out that a yard of walk measured along the middle represents a square yard of garden, "whether we consider the straight stretches of walk or the square yards at the angles, in which the middle line goes half a yard in one direction and then turns a right angle and goes half a yard in another direction."