have no great weight with you, but I hope you will feel that it would be as well not to employ it, unless you are quite certain of being correct yourself.' The only instances the writer gives of the `trenchant expressions' are `hapless' and `malefactors'. I beg to assure him (and any others who may need the assurance: I trust there are none) that all such words have been used in jest, and with no idea that they could possibly annoy any one, and that I sincerely regret any annoyance I may have thus inadvertently given. May I hope that in future they will recognise the distinction between severe language used in sober earnest, and the `words of unmeant bitterness', which Coleridge has alluded to in that lovely passage beginning, `A little child, a limber elf'? If the writer will refer to that passage, or to the Preface to Fire, Famine, and Slaughter, he will find the distinction, for which I plead, far better drawn out than I could hope to do in any words of mine.
The writer's insinuation that I care not how much annoyance I give to my readers I think it best to pass over in silence; but to his concluding remark I must entirely demur. I hold that to use language likely to annoy any of my correspondents would not be in the least justified by the plea that I was `quite certain of being correct'. I trust that the knot-untiers and I are not on such terms as those!
I beg to thank G.B. for the offer of a puzzle--which, however, is too like the old one, `Make four 9's into 100'.
Problem. Place twenty-four pigs in four sties so that, as you go round and round, you may always find the number in each sty nearer to ten than the number in the last.
Answer. Place 8 pigs in the first sty, 10 in the second, nothing in the third, and 6 in the fourth: 10 is nearer ten than 8; nothing is nearer ten than 10; 6 is nearer ten than nothing; and 8 is nearer ten than 6.
This problem is noticed by only two correspondents. BALBUS says, `It certainly cannot be solved mathematically, nor do I see how to solve it by any verbal quibble.' NOLENS VOLENS makes Her Radiancy change the direction of going round; and even then is obliged to add, `the pig must be carried in front of her'!
Problem. Omnibuses start from a certain point, both ways, every 15 minutes. A traveler, starting on foot along with one of them, meets one in 12 ½ minutes: when will he be overtaken by one?
Answer. In 6 ¼ minutes.
Solution. Let `a' be the distance an omnibus goes in 15 minutes, and `x' the distance from the starting-
point to where the traveler is overtaken. Since the omnibus met is due at the starting-point in 2 ½ minutes,
it goes in that time as far as the traveler walks in 12 ½, i.e., it goes 5 times as fast. Now the overtaking
omnibus is `a' behind the traveler when he starts, and therefore
a
goes `a + x' while he goes `x'. Hence a
+ x = 5x; i.e. 4x = a, and x =---. This distance would be
4
15 15
traversed by an omnibus in --- minutes,
and therefore by the traveler in 5 x ---. Hence he is
4 4
overtaken in 18 3/4 minutes after starting, i.e. in
6 ¼ minutes after meeting the omnibus.
Four answers have been received, of which two are wrong. DINAH MITE rightly states that the overtaking omnibus reached the point where they met the other omnibus 5 minutes after they left, but wrongly concludes that, going 5 times as fast, it would overtake them in another minute. The travelers are 5 minutes' walk ahead of the omnibus, and must walk ¼ of this distance farther before the omnibus overtakes them, which will be 1/5 of the distance traversed by the omnibus in the same time: this will require 1 ¼ minutes more. NOLENS VOLENS tries it by a process like `Achilles and the Tortoise'. He rightly states that, when the overtaking omnibus leaves the gate, the travelers are 1/5 of `a' ahead, and that it will take the omnibus 3