rest all do it, wholly or
partly, by guess-work.

The problem is of course (as any Algebraist sees at once) a case of
"simultaneous simple equations." It is, however, easily soluble by
Arithmetic only; and, when this is the case, I hold that it is bad
workmanship to use the more complex method. I have not, this time, given
more credit to arithmetical solutions; but in future problems I shall
(other things being equal) give the highest marks to those who use the
simplest machinery. I have put into Class I. those whose answers seemed
specially short and neat, and into Class III. those that seemed
specially long or clumsy. Of this last set, A. C. M., FURZE-BUSH, JAMES,
PARTRIDGE, R. W., and WAITING FOR THE TRAIN, have sent long wandering
solutions, the substitutions having no definite method, but seeming to
have been made to see what would come of it. CHILPOME and DUBLIN BOY
omit some of the working. ARVON MARLBOROUGH BOY only finds the weight of
_one_ sack.

CLASS LIST

I.

B. E. D.
C. H.
CONSTANCE JOHNSON.
GREYSTEAD.
GUY.
HOOPOE.
J. F. A.
M. A. H.
NUMBER FIVE.
PEDRO.
R. E. X.
SEVEN OLD MEN.
VIS INERTIAE.
WILLY B.
YAHOO.

II.

AMERICAN SUBSCRIBER.
AN APPRECIATIVE SCHOOLMA'AM.
AYR.
BRADSHAW OF THE FUTURE.
CHEAM.
C. M. G.
DINAH MITE.
DUCKWING.
E. C. M.
E. N. Lowry.
ERA.
EUROCLYDON.
F. H. W.
FIFEE.
G. E. B.
HARLEQUIN.
HAWTHORN.
HOUGH GREEN.
J. A. B.
JACK TAR.
J. B. B.
KGOVJNI.
LAND LUBBER.
L. D.
MAGPIE.
MARY.
MHRUXI.
MINNIE.
MONEY-SPINNER.
NAIRAM.
OLD CAT.
POLICHINELLE.
SIMPLE SUSAN.
S. S. G.
THISBE.
VERENA.
WAMBA.
WOLFE.
WYKEHAMICUS.
Y. M. A. H.

III.

A. C. M.
ARVON MARLBOROUGH BOY.
CHILPOME.
DUBLIN BOY.
FURZE-BUSH.
JAMES.
PARTRIDGE.
R. W.
WAITING FOR THE TRAIN.

ANSWERS TO KNOT V.

_Problem._--To mark pictures, giving 3 x's to 2 or 3, 2 to 4 or 5, and 1
to 9 or 10; also giving 3 o's to 1 or 2, 2 to 3 or 4 and 1 to 8 or 9; so
as to mark the smallest possible number of pictures, and to give them
the largest possible number of marks.

_Answer._--10 pictures; 29 marks; arranged thus:--

x x x x x x x x x o
x x x x x o o o o
x x o o o o o o o o

_Solution._--By giving all the x's possible, putting into brackets the
optional ones