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
1. BRADSHAW OF THE FUTURE CAIUS CLIFTON C. MARTREB
2. MATTHEW MATTICKS
3. CHEAM CROPHI AND MOPHI E. R. D. L.
{RAGS AND TATTERS MEGGY POTTS
{MAD HATTER
A remonstrance has reached me from SCRUTATOR on the subject of Knot 1, 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.
Problem. (1) Two travelers, 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 traveler counting as `one' the train containing the other traveler. How many did each meet?
Answers. (1) 19. (2) The easterly traveler met 12; the other 8.
The trains one way took 180 minutes, the other way 120. Let us take the 1.c.m., 360, and divide the railway into 360 units. Then one set of trains went at the rate of 2 units a minute and at intervals of 30 units; the other at the rate of 3 units a minute and at intervals of 45 units. An easterly train starting has 45 units between it and the first train it will meet: it does 2/5 of this while the other does 3/5, and thus meets it at the end of 18 units, and so all the way round. A westerly train starting has 30 units between it and the first train it will meet: it does 3/5 of this while the other does 2/5, and thus meets it at the end of 18 units, and so all the way round. Hence if the railway be divided, by 19 posts, into 20 parts, each containing 18 units, trains meet at every post, and, in (1) each traveler passes 19 posts in going round, and so meets 19 trains. But, in (2), the easterly traveler only begins to count after traversing 2/5 of the journey, i.e. on reaching the 8th post, and so counts 12 posts: similarly, the other counts 8. They meet at the end of 2/5 of 3 hours, or 3/5 of 2 hours, i.e. 72 minutes.
Forty-five answers have been received. Of these, 12 are beyond the reach of discussion, as they give no working. I can but enumerate their names, ARDMORE, E.A., F.A.D., L.D., MATTHEW MATTICKS, M.E.T., POC-POO, and THE RED QUEEN are all wrong. BETA and ROWENA have got (1) right and (2) wrong. CHEEKY BOB and NAIRAM give the right answers, but it may perhaps make the one less cheeky, and induce the other to take a less inverted view of things, to be informed that, if this had been a competition for a prize, they would have got no marks. (N.B.--I have not ventured to put E.A.'s name in full, as she only gave it provisionally, in case her answer should prove right.)
Of the 33 answers for which the working is given, 10 are wrong; 11 half-wrong and half-right; 3 right, except that they cherish the delusion that it was Clara who traveled in the easterly train--a point which the data do not enable us to settle; and 9 wholly right.