THE RED QUEEN.
WALL-FLOWER.

Sec. 3 (4 _steps_).

HAWTHORN.
JORAM.
S. S. G.

Sec. 4 (5 _steps_).

A STEPNEY COACH.

Sec. 5 (6 _steps_).

BAY LAUREL.
BRADSHAW OF THE FUTURE.

Sec. 6 (9 _steps_).

OLD KING COLE.

Sec. 7 (14 _steps_).

THESEUS.

ANSWERS TO CORRESPONDENTS.

I have received several letters on the subjects of Knots II. and VI.,
which lead me to think some further explanation desirable.

In Knot II., I had intended the numbering of the houses to begin at one
corner of the Square, and this was assumed by most, if not all, of the
competitors. TROJANUS however says "assuming, in default of any
information, that the street enters the square in the middle of each
side, it may be supposed that the numbering begins at a street." But
surely the other is the more natural assumption?

In Knot VI., the first Problem was of course a mere _jeu de mots_, whose
presence I thought excusable in a series of Problems whose aim is to
entertain rather than to instruct: but it has not escaped the
contemptuous criticisms of two of my correspondents, who seem to think
that Apollo is in duty bound to keep his bow always on the stretch.
Neither of them has guessed it: and this is true human nature. Only the
other day--the 31st of September, to be quite exact--I met my old friend
Brown, and gave him a riddle I had just heard. With one great effort of
his colossal mind, Brown guessed it. "Right!" said I. "Ah," said he,
"it's very neat--very neat. And it isn't an answer that would occur to
everybody. Very neat indeed." A few yards further on, I fell in with
Smith and to him I propounded the same riddle. He frowned over it for a
minute, and then gave it up. Meekly I faltered out the answer. "A poor
thing, sir!" Smith growled, as he turned away. "A very poor thing! I
wonder you care to repeat such rubbish!" Yet Smith's mind is, if
possible, even more colossal than Brown's.

The second Problem of Knot VI. is an example in ordinary Double Rule of
Three, whose essential feature is that the result depends on the
variation of several elements, which are so related to it that, if all
but one be constant, it varies as that one: hence, if none be constant,
it varies as their product. Thus, for example, the cubical contents of a
rectangular tank vary as its length, if breadth and depth be constant,
and so on; hence, if none be constant, it varies as the product of the
length, breadth, and dept