Answers to Knot 4

Problem. — There are 5 sacks, of which Nos. 1, 2, weigh 12 lbs.; Nos. 2, 3, 13½ lbs.; Nos. 3, 4, 11½ lbs.; Nos. 4; 5, 8 lbs.; Nos. 1, 3, 5, 16 lbs. Required the weight of each sack.

Answer. — 5½, 6½, 7, 4½, 3½.

The sum of all the weighings, 61 lbs., includes sack No. 3 thrice and each other twice. Deducting¹ 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 6½ lbs., 4½ lbs. for Nos. 2, 4; and hence again, the 1st and 4th weighings give 5½ lbs., 3½ lbs., for Nos. 1, 5. 1

Ninety-seven answers have been received. Of these, 15 are beyond the reach of discussion, as they give no working. I can but enumerate² their names, and I take this opportunity of saying that this is the last time I shall put on record the names of competitors who give no sort of clue to the process by which their answers were obtained. In guessing a conundrum³, or in catching⁴ a flea⁵, we do not expect the breathless victor to give us afterwards, in cold blood, a history of the mental or muscular efforts by which he achieved success; but a mathematical calculation is another thing. The names of this “mute inglorious” band are Common Sense, D. E. R., Douglas, E. L., Ellen, I. M. T., J. M. C., Joseph, Knot I, Lucy, Meek⁶, M. F. C., Pyramus, Shah, Veritas.

Of the eighty-two answers with which the working, or some approach to it, is supplied, one is wrong: seventeen have given solutions which are (from one cause or another) practically valueless: the remaining sixty-four I shall try to arrange in a Class List, according to the varying degrees of shortness and neatness to which they seem to have attained⁷.

The solitary⁸ wrong answer is from Nell. To be thus “alone in a crowd” is a distinction — a painful one, no doubt, but still a distinction. I am sorry for you, my dear young lady, and I seem to hear your tearful exclamation¹⁰, when you read these lines, “Ah! This is the knell¹¹ of all my hopes!” Why, oh why, did you assume that the 4th and 5th bags weighed 4 lbs. each? And why did you not test your answers? However, please try again: and please don’t change your nom-de-plume: let us have Nell in the First Class next time!

The seventeen whose solutions are practically valueless are Ardmore, A Ready Reckoner, Arthur, Bog-Lark, Bog-Oak, Bridget, First Attempt, J. L. C., M. E. T., Rose, Rowena, Sea-Breeze, Sylvia, Thistledown, Three-Fifths Asleep, Vendredi, and Winifred. Bog-Lark tries it by a sort of “rule of false”, assuming experimentally that Nos. 1, 2, weigh 6 lbs. each, and having thus produced 17½ instead of 16, as the weight of 1, 3, and 5, she removes “the superfluous¹² pound and a half”, but does not explain how she knows from which to take it. Three-Fifths Asleep says that (when in that peculiar¹³ state) “it seemed perfectly¹⁴ clear” to her that, “3 out of the 5 sacks being weighed twice over, 3/5 of 45=27, must be the total weight of the 5 sacks.” As to which I can only say, with the Captain, “it beats me entirely¹⁵!” Winifred, on the plea that “one must have a starting-point”, assumes (what I fear is a mere¹⁶ guess) that No. 1 weighed 59 lbs. The rest all do it, wholly or partly, by guess-work.

The problem is of course (as any algebraist¹⁷ sees at once) a case of “simultaneous simple equations” It is, however, easily soluble¹⁸ 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 machinery¹⁹. I have put into Class I those whose answers seemed specially²⁰ 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, TC. W., and Waiting for the Train, have sent long wandering solutions, the substitutions have 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 Marleborough 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 Subscriber²¹.
An Appreciative²² School-Ma’am.
Ayr.
Bradshaw of the Future.
Cheam.
C. M. G.
Dinah Mite²³.
Duckwing.
E. C. M.
E. N. Lowry.
Era.
Euroclydon.
F. H. W.
Fifee.
G. E. B.
Harlequin.
Hawthorn²⁴.
Hough Green.
J. A. B.
Jack²⁵ Tar⁹.
J. B. B.
Kgovjni.
Land Lubber.
L. D.
Magpie²⁶.
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 Marleborough Boy.
Chilpome.
Dublin Boy.
Furze-Bush.
James.
Partridge.
R. W.
Waiting for the Train.

1 deducting   

v.扣除，减去( deduct的现在分词 )

参考例句：

• Deducting drop size and velocity from circular blood stains. 如何从循环的血液中降低血滴的大小和速度。 来自电影对白
• Ordinary shareholders receive dividend from profit after deducting the preference shares dividend. 普通股股东可获派剩馀的盈利为股息。 来自互联网

2 enumerate   

v.列举，计算，枚举，数

参考例句：

• The heroic deeds of the people's soldiers are too numerous to enumerate.人民子弟兵的英雄事迹举不胜举。
• Its applications are too varied to enumerate.它的用途不胜枚举。

3 conundrum   

n.谜语；难题

参考例句：

• Let me give you some history about a conundrum.让我给你们一些关于谜题的历史。
• Scientists had focused on two explanations to solve this conundrum.科学家已锁定两种解释来解开这个难题。

4 catching   

adj.易传染的，有魅力的，迷人的，接住

参考例句：

• There are those who think eczema is catching.有人就是认为湿疹会传染。
• Enthusiasm is very catching.热情非常富有感染力。

5 flea   

n.跳蚤

参考例句：

• I'll put a flea in his ear if he bothers me once more.如果他再来打扰的话，我就要对他不客气了。
• Hunter has an interest in prowling around a flea market.亨特对逛跳蚤市场很感兴趣。

6 meek   

adj.温顺的，逆来顺受的

参考例句：

• He expects his wife to be meek and submissive.他期望妻子温顺而且听他摆布。
• The little girl is as meek as a lamb.那个小姑娘像羔羊一般温顺。

7 attained   

（通常经过努力）实现( attain的过去式和过去分词 )； 达到； 获得； 达到（某年龄、水平、状况）

参考例句：

• She has attained the degree of Master of Arts. 她已获得文学硕士学位。
• Lu Hsun attained a high position in the republic of letters. 鲁迅在文坛上获得崇高的地位。

8 solitary   

adj.孤独的，独立的，荒凉的；n.隐士

参考例句：

• I am rather fond of a solitary stroll in the country.我颇喜欢在乡间独自徜徉。
• The castle rises in solitary splendour on the fringe of the desert.这座城堡巍然耸立在沙漠的边际，显得十分壮美。

9 tar   

n.柏油，焦油；vt.涂或浇柏油/焦油于

参考例句：

• The roof was covered with tar.屋顶涂抹了一层沥青。
• We use tar to make roads.我们用沥青铺路。

10 exclamation   

n.感叹号，惊呼，惊叹词

参考例句：

• He could not restrain an exclamation of approval.他禁不住喝一声采。
• The author used three exclamation marks at the end of the last sentence to wake up the readers.作者在文章的最后一句连用了三个惊叹号，以引起读者的注意。

11 knell   

n.丧钟声；v.敲丧钟

参考例句：

• That is the death knell of the British Empire.这是不列颠帝国的丧钟。
• At first he thought it was a death knell.起初，他以为是死亡的丧钟敲响了。

12 superfluous   

adj.过多的，过剩的，多余的

参考例句：

• She fined away superfluous matter in the design. 她删去了这图案中多余的东西。
• That request seemed superfluous when I wrote it.我这样写的时候觉得这个请求似乎是多此一举。

13 peculiar   

adj.古怪的，异常的；特殊的，特有的

参考例句：

• He walks in a peculiar fashion.他走路的样子很奇特。
• He looked at me with a very peculiar expression.他用一种很奇怪的表情看着我。

14 perfectly   

adv.完美地，无可非议地，彻底地

参考例句：

• The witnesses were each perfectly certain of what they said.证人们个个对自己所说的话十分肯定。
• Everything that we're doing is all perfectly above board.我们做的每件事情都是光明正大的。

15 entirely   

ad.全部地，完整地；完全地，彻底地

参考例句：

• The fire was entirely caused by their neglect of duty. 那场火灾完全是由于他们失职而引起的。
• His life was entirely given up to the educational work. 他的一生统统献给了教育工作。

16 mere   

adj.纯粹的；仅仅，只不过

参考例句：

• That is a mere repetition of what you said before.那不过是重复了你以前讲的话。
• It's a mere waste of time waiting any longer.再等下去纯粹是浪费时间。

17 algebraist   

n.代数学家

参考例句：

18 soluble   

adj.可溶的；可以解决的

参考例句：

• These tablets are soluble in water.这些药片可在水中溶解。
• Camphor is soluble in alcohol.樟脑在酒精中可以溶化。

19 machinery   

n.(总称)机械，机器；机构

参考例句：

• Has the machinery been put up ready for the broadcast?广播器材安装完毕了吗？
• Machinery ought to be well maintained all the time.机器应该随时注意维护。

20 specially   

adv.特定地；特殊地；明确地

参考例句：

• They are specially packaged so that they stack easily.它们经过特别包装以便于堆放。
• The machine was designed specially for demolishing old buildings.这种机器是专为拆毁旧楼房而设计的。

21 subscriber   

n.用户，订户；（慈善机关等的）定期捐款者；预约者；签署者

参考例句：

• The subscriber to a government loan has got higher interest than savings. 公债认购者获得高于储蓄的利息。 来自辞典例句
• Who is the subscriber of that motto? 谁是那条座右铭的签字者？ 来自辞典例句

22 appreciative   

adj.有鉴赏力的，有眼力的；感激的

参考例句：

• She was deeply appreciative of your help.她对你的帮助深表感激。
• We are very appreciative of their support in this respect.我们十分感谢他们在这方面的支持。

23 mite   

n.极小的东西；小铜币

参考例句：

• The poor mite was so ill.可怜的孩子病得这么重。
• He is a mite taller than I.他比我高一点点。

24 hawthorn   

山楂

参考例句：

• A cuckoo began calling from a hawthorn tree.一只布谷鸟开始在一株山楂树里咕咕地呼叫。
• Much of the track had become overgrown with hawthorn.小路上很多地方都长满了山楂树。

25 jack   

n.插座，千斤顶，男人；v.抬起，提醒，扛举；n.（Jake）杰克

参考例句：

• I am looking for the headphone jack.我正在找寻头戴式耳机插孔。
• He lifted the car with a jack to change the flat tyre.他用千斤顶把车顶起来换下瘪轮胎。

26 magpie   

n.喜欢收藏物品的人，喜鹊，饶舌者

参考例句：

• Now and then a magpie would call.不时有喜鹊的叫声。
• This young man is really a magpie.这个年轻人真是饶舌。