l. The others all get "18" in
various ways. BOG-OAK, GUY, and R. W. divide the trains which the
westerly traveller has to meet into 2 sets, viz., those already on the
line, which they (rightly) make "11," and those which started during her
2 hours' journey (exclusive of train met on arrival), which they
(wrongly) make "7"; and they make a similar mistake with the easterly
train. BRIDGET (rightly) says that the westerly traveller met a train
every 6 minutes for 2 hours, but (wrongly) makes the number "20"; it
should be "21." G. E. B. adopts BO-PEEP'S method, but (wrongly) strikes
out (for the easterly traveller) the train which started at the
_commencement_ of the previous 2 hours. MARY thinks a train, met on
arrival, must not be counted, even when met on a _previous_ occasion.

The 3, who are wholly right but for the unfortunate "Clara" theory, are
F. LEE, G. S. C., and X. A. B.

And now "descend, ye classic Ten!" who have solved the whole problem.
Your names are AIX-LES-BAINS, ALGERNON BRAY (thanks for a friendly
remark, which comes with a heart-warmth that not even the Atlantic could
chill), ARVON, BRADSHAW OF THE FUTURE, FIFEE, H. L. R., J. L. O., OMEGA,
S. S. G., and WAITING FOR THE TRAIN. Several of these have put Clara,
provisionally, into the easterly train: but they seem to have understood
that the data do not decide that point.

CLASS LIST.

I.

AIX-LES-BAINS.
ALGERNON BRAY.
BRADSHAW OF THE FUTURE.
FIFEE.
H. L. R.
OMEGA.
S. S. G.
WAITING FOR THE TRAIN.

II.

ARVON.
J. L. O.

III.

F. LEE.
G. S. C.
X. A. B.

ANSWERS TO KNOT IV.

_Problem._--"There are 5 sacks, of which Nos. 1, 2, weigh 12 lbs.; Nos.
2, 3, 13-1/2 lbs.; Nos. 3, 4, 11-1/2 lbs.; Nos. 4, 5, 8 lbs.; Nos. 1, 3,
5, 16 lbs. Required the weight of each sack."

_Answer._--"5-1/2, 6-1/2, 7, 4-1/2, 3-1/2."

* * * * *

The sum of all the weighings, 61 lbs., includes sack No. 3 _thrice_ and
each other _twice_. Deducting twice the sum of the 1st and 4th
weighings, we get 21 lbs. for _thrice_ No. 3, _i.e._, 7 lbs. for No. 3.
Hence, the 2nd and 3rd weighings give 6-1/2 lbs., 4-1/2 lbs. for Nos. 2,
4; and hence again, the 1st and 4th weighings give 5-1/2 lbs., 3-1/2
lbs., for Nos. 1, 5.

* * * * *

Ninety-seven answers have been received. Of these, 15 are beyond the
reach of discussion, as they give no working. I can but enumerate