milarly, for the second, try Nos. 1, 30, 51, 71.)

Of the five partly-right solutions, RAGS AND TATTERS and MAD HATTER (who
send one answer between them) make No. 25 6 units from the corner
instead of 5. CHEAM, E. R. D. L., and MEGGY POTTS leave openings at the
corners of the Square, which are not in the _data_: moreover CHEAM gives
values for the distances without any hint that they are only
_approximations_. CROPHI AND MOPHI make the bold and unfounded
assumption that there were really 21 houses on each side, instead of 20
as stated by Balbus. "We may assume," they add, "that the doors of Nos.
21, 42, 63, 84, are invisible from the centre of the Square"! What is
there, I wonder, that CROPHI AND MOPHI would _not_ assume?

Of the five who are wholly right, I think BRADSHAW OF THE FUTURE, CAIUS,
CLIFTON C., and MARTREB deserve special praise for their full
_analytical_ solutions. MATTHEW MATTICKS picks out No. 9, and proves it
to be the right house in two ways, very neatly and ingeniously, but
_why_ he picks it out does not appear. It is an excellent _synthetical_
proof, but lacks the analysis which the other four supply.

CLASS LIST.

I.

BRADSHAW OF THE FUTURE
CAIUS.
CLIFTON C.
MARTREB.

II.

MATTHEW MATTICKS.

III.

CHEAM.
CROPHI AND MOPHI.
E. R. D. L.
MEGGY POTTS.
{RAGS AND TATTERS.
{MAD HATTER.

A remonstrance has reached me from SCRUTATOR on the subject of KNOT I.,
which he declares was "no problem at all." "Two questions," he says,
"are put. To solve one there is no data: the other answers itself." As
to the first point, SCRUTATOR is mistaken; there _are_ (not "is") data
sufficient to answer the question. As to the other, it is interesting to
know that the question "answers itself," and I am sure it does the
question great credit: still I fear I cannot enter it on the list of
winners, as this competition is only open to human beings.

ANSWERS TO KNOT III.

_Problem._--(1) "Two travellers, starting at the same time, went
opposite ways round a circular railway. Trains start each way every 15
minutes, the easterly ones going round in 3 hours, the westerly in 2.
How many trains did each meet on the way, not counting trains met at the
terminus itself?" (2) "They went round, as before, each traveller
counting as 'one' the train containing the other traveller. How many did
each meet?"

_Answers._--(1) 19. (2) The easterly traveller met 12; the other 8.