m of _x_-1/2, _x_-1/2, _x_-1,
_x_-1, _i.e._ 4_x_-3: but the fourth term should be _x_-1-1/2, so that
her first coil is 1/2 a yard too long. Her second coil is the sum of
_x_-2-1/2, _x_-2-1/2, _x_-3, _x_-3: here the first term should be _x_-2
and the last _x_-3-1/2: 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 ETONAE attempts to prove what C. G. L. assumes by a particular
instance, taking a garden 6 by 5-1/2. He ought to have proved it
generally: what is true of one number is not always true of others. OLD
KING COLE solves it by an Arithmetical Progression. It is right, but too
lengthy to be worth as much as a Quadratic.

VINDEX 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."

CLASS LIST.

I.

VINDEX.

II.

ALUMNUS ETONAE.
OLD KING COLE.

III.

DINAH MITE.
JANET.
MAGPIE.
TAFFY.

ANSWERS TO KNOT X.

Sec. 1. THE CHELSEA PENSIONERS.

_Problem._--If 70 per cent. have lost an eye, 75 per cent. an ear, 80
per cent. an arm, 85 per cent. a leg: what percentage, _at least_, must
have lost all four?

_Answer._--Ten.

_Solution._--(I adopt that of POLAR STAR, as being better than my own).
Adding the wounds together, we get 70 + 75 + 80 + 85 = 310, among 100
men; which gives 3 to each, and 4 to 10 men. Therefore the least
percentage is 10.

* * * * *

Nineteen answers have been received. One is "5," but, as no working is
given with it, it must, in accordance with the rule, remain "a deed
without a name." JANET makes it "35 and 7/10ths." I am sorry she has
misunderstood the question, and has supposed that those who had los