Answers to Knot 6

Problem 1. — A and B began the year with only £1000 apiece. They borrowed nought¹; they stole nought. On the next New Year’s Day they had £60,000 between them. How did they do it?

Solution. — They went that day to the Bank of England. A stood in front of it, while B went round and stood behind it.

Two answers have been received, both worthy² of much honour. Addlepate makes them borrow “zero” and steal “zero”, and uses both cyphers by putting them at the righthand end of the £1000, thus producing £100,000, which is well over the mark. But (or to express it in Latin) At Spes Infracta has solved it even more ingeniously: with the first cypher she turns the “1” of the £1000 into a “9”, and adds the result to the original sum, thus getting £10,000: and in this, by means of the other “zero”, she turns the “1” into a “6” thus hitting the exact £60,000.

Class List

I.

At Spes Infracta.

II.

Addlepate.

Problem 2. — L makes 5 scarves, while M makes 2: Z makes 4, while L makes 3. Five scarves of Z’s weigh one of L’s; 5 of M’s weigh 3 of Z’s. One of M’s is as warm as 4 of Z’s and one of L’s as warm as 3 of M’s. Which is best, giving equal weight in the result of rapidity of work, lightness, and warmth?

Answer. — The order is M, L, Z.

Solution. — As to rapidity (other things being constant), L’s merit is to M’s in the ratio of 5 to 2: Z’s to L’s in the ratio of 4 to 3. In order to get one set of 3 numbers fulfilling these conditions, it is perhaps simplest to take the one that occurs twice as unity³, and reduce the others to fractions: this gives, for L, M, and Z, the marks 1, 2/3, 4/3. In estimating for lightness we observe that the greater the weight, the less the merit, so that Z’s merit is to L’s as 5 to 1. Thus the marks for lightness are 1/5, 5/3, 1. And similarly, the marks for warmth are 3, 1, 1/4. To get the total result, we must multiply L’s 3 marks together, and do the same for M and for Z. The final numbers are 1 x 1/5 x 3, 2/5 x 5/3 x 1, 4/3 x 1 x 1/4; i. e. 3/5, 2/3, 1/3; i. e. multiplying throughout by 15 (which will not alter the proportion), 9, 10, 5, showing the order of merit to be M, L, Z.

Twenty-nine answers have been received, of which five are right, and twenty-four wrong. These hapless ones have all (with three exceptions) fallen into the error of adding the proportional numbers together, for each candidate, instead of multiplying. Why the latter is right, rather than the former, is fully⁵ proved in textbooks, so I will not occupy space by stating it here: but it can be illustrated⁶ very easily by the case of length, breadth, and depth. Suppose A and B are rival diggers of rectangular tanks: the amount of work done is evidently measured by the number of cubical feet dug out. Let A dig a tank 10 feet long, 10 wide, 2 deep: let B dig one 6 feet long, 5 wide, 10 deep. The cubical contents are 200, 300; i.e. B is best digger in the ratio of 3 to 2. Now try marking for length, width, and depth, separately; giving a maximum mark of 10 to the best in each contest, and then adding the results!

Of the twenty-four malefactors, one gives no working, and so has no real claim to be named; but I break the rule for once, in deference⁷ to its success in Problem 1: he, she, it, is Addlepate. The other twenty-three may be divided into five groups.

First and worst are, I take it, those who put the rightful winner last; arranging them as “Lolo, Zuzu, Mimi”. The names of these desperate wrong-doers are Ayr, Bradshaw of the Future, Furze-Bush, and Pollux (who send a joint⁸ answer), Greystead, Guy, Old Hen, and Simple Susan. The latter was once best of all; the Old Hen has taken advantage of her simplicity⁹, and beguiled¹⁰ her with the chaff¹¹ which was the bane of her own chickenhood.

Secondly¹², I point the finger of scorn at those who have put the worst candidate at the top; arranging them as “Zuzu, Mimi, Lolo”. They are Graecia, M. M., Old Cat, and R. E. X. “’Tis Greece, but — ”

The third set have avoided both these enormities, and have even succeeded in putting the worst last, their answer being “Lolo, Mimi, Zuzu”. Their names are Ayr (who also appears among the “quite too too”, Clifton C., F. B., Fiffee, Grig, Janet, and Mrs. Sairey Gamp. F. B. has not fallen into the common error; she multiplies together the proportionate number she gets, but in getting them she goes wrong, by reckoning warmth as a demerit. Possibly she is “Freshly Burnt”, or comes “From Bombay” Janet and Mrs. Sairey Gamp have also avoided this error: the method thev have adopted is shrouded¹³ in mystery — I scarcely feel competent to criticise¹⁴ it. Mrs. Gamp says, “If Zuzu makes 4 while Lolo makes 3, Zuzu makes 6 while Lolo makes 5 [bad reasoningl, while Mimi makes 2.” From this she concludes, “Therefore Zuzu excels in speed by 1” (i.e. when compared with Lolo? but what about Mimi!). She then compares the 3 kinds of excellence¹⁵, measured on this mystic scale. Janet takes the statement that “Lolo makes 5 while Mimi makes 2”, to prove that “Lolo makes 3 while Mimi makes 1 and Zuzu 4” (worse reasoning than Mrs. Gamp’s), and thence concludes that “Zuzu excels in speed by 1/8”! Janet Should have been Adeline, “mystery of mysteries!”

The fourth set actually put Mimi at the top, arranging them as “Mimi, Zuzu, Lolo”. They are Marquis And Co., Martreb, S. B. B. (first initial scarcely legible: may be meant for “J”), and Stanza¹⁶.

The fifth set consists of An Ancient Fish and Camel. These ill-assorted comrades, by dint¹⁷ of foot and fin⁴, have scrambled¹⁸ into the right answer, but, as their method is wrong, of course it counts for nothing. Also An Ancient Fish, has very ancient and fishlike ideas as to how, numbers represent merit: she says, “Lolo gains 2½ on Mimi.” Two and a half what? Fish, fish, art thou in thy duty?

Of the five winners I put Balbus and The Elder Traveller slightly below the other three Balbus for defective¹⁹ reasoning, the other for scanty²⁰ working. Balbus gives two reasons for saying; that addition of marks is not the right method, and then adds, “It follows that the decision must be made by multiplying the marks together”. This is hardly more logical than to say, “This is not Spring: therefore it must be Autumn”.

Class List.

I.

Dinah Mite²¹.
E. B. D. L.
Joram.

II.

Balbus.
The Elder Traveller.

With regard to Knot V, I beg to express to Vis Inertiae and to any others, who, like her, understood the condition to be that every marked picture must have three marks, my sincere regret that the unfortunate phrase “fill the columns with oughts and crosses” should have caused them to waste so much time and trouble. I can only repeat that a literal interpretstion of “fill” would seem to me to require that every picture in the gallery should be marked. Vis Inertiae would have been in the First Class if she had sent in the solution she now offers.

1 nought   

n.／adj.无，零

参考例句：

• We must bring their schemes to nought.我们必须使他们的阴谋彻底破产。
• One minus one leaves nought.一减一等于零。

2 worthy   

adj.(of)值得的，配得上的；有价值的

参考例句：

• I did not esteem him to be worthy of trust.我认为他不值得信赖。
• There occurred nothing that was worthy to be mentioned.没有值得一提的事发生。

3 unity   

n.团结，联合，统一；和睦，协调

参考例句：

• When we speak of unity,we do not mean unprincipled peace.所谓团结，并非一团和气。
• We must strengthen our unity in the face of powerful enemies.大敌当前，我们必须加强团结。

4 fin   

n.鳍；(飞机的)安定翼

参考例句：

• They swim using a small fin on their back.它们用背上的小鳍游动。
• The aircraft has a long tail fin.那架飞机有一个长长的尾翼。

5 fully   

adv.完全地，全部地，彻底地；充分地

参考例句：

• The doctor asked me to breathe in,then to breathe out fully.医生让我先吸气，然后全部呼出。
• They soon became fully integrated into the local community.他们很快就完全融入了当地人的圈子。

6 illustrated   

adj. 有插图的，列举的 动词illustrate的过去式和过去分词

参考例句：

• His lecture was illustrated with slides taken during the expedition. 他在讲演中使用了探险时拍摄到的幻灯片。
• The manufacturing Methods: Will be illustrated in the next chapter. 制作方法将在下一章说明。

7 deference   

n.尊重，顺从；敬意

参考例句：

• Do you treat your parents and teachers with deference?你对父母师长尊敬吗？
• The major defect of their work was deference to authority.他们的主要缺陷是趋从权威。

8 joint   

adj.联合的，共同的；n.关节，接合处；v.连接，贴合

参考例句：

• I had a bad fall,which put my shoulder out of joint.我重重地摔了一跤，肩膀脫臼了。
• We wrote a letter in joint names.我们联名写了封信。

9 simplicity   

n.简单，简易；朴素；直率，单纯

参考例句：

• She dressed with elegant simplicity.她穿着朴素高雅。
• The beauty of this plan is its simplicity.简明扼要是这个计划的一大特点。

10 beguiled   

v.欺骗( beguile的过去式和过去分词 )；使陶醉；使高兴；消磨（时间等）

参考例句：

• She beguiled them into believing her version of events. 她哄骗他们相信了她叙述的事情。
• He beguiled me into signing this contract. 他诱骗我签订了这项合同。 来自《现代英汉综合大词典》

11 chaff   

v.取笑，嘲笑；n.谷壳

参考例句：

• I didn't mind their chaff.我不在乎他们的玩笑。
• Old birds are not caught with chaff.谷糠难诱老雀。

12 secondly   

adv.第二，其次

参考例句：

• Secondly,use your own head and present your point of view.第二，动脑筋提出自己的见解。
• Secondly it is necessary to define the applied load.其次，需要确定所作用的载荷。

13 shrouded   

v.隐瞒( shroud的过去式和过去分词 )；保密

参考例句：

• The hills were shrouded in mist . 这些小山被笼罩在薄雾之中。
• The towers were shrouded in mist. 城楼被蒙上薄雾。 来自《简明英汉词典》

14 criticise   

v.批评，评论；非难

参考例句：

• Right and left have much cause to criticise government.左翼和右翼有很多理由批评政府。
• It is not your place to criticise or suggest improvements!提出批评或给予改进建议并不是你的责任！

15 excellence   

n.优秀，杰出，(pl.)优点，美德

参考例句：

• His art has reached a high degree of excellence.他的艺术已达到炉火纯青的地步。
• My performance is far below excellence.我的表演离优秀还差得远呢。

16 stanza   

n.（诗）节，段

参考例句：

• We omitted to sing the second stanza.我们漏唱了第二节。
• One young reporter wrote a review with a stanza that contained some offensive content.一个年轻的记者就歌词中包含有攻击性内容的一节写了评论。

17 dint   

n.由于，靠；凹坑

参考例句：

• He succeeded by dint of hard work.他靠苦干获得成功。
• He reached the top by dint of great effort.他费了很大的劲终于爬到了顶。

18 scrambled   

v.快速爬行( scramble的过去式和过去分词 )；攀登；争夺；（军事飞机）紧急起飞

参考例句：

• Each scrambled for the football at the football ground. 足球场上你争我夺。 来自《现代汉英综合大词典》
• He scrambled awkwardly to his feet. 他笨拙地爬起身来。 来自《简明英汉词典》

19 defective   

adj.有毛病的，有问题的，有瑕疵的

参考例句：

• The firm had received bad publicity over a defective product. 该公司因为一件次品而受到媒体攻击。
• If the goods prove defective, the customer has the right to compensation. 如果货品证明有缺陷， 顾客有权索赔。

20 scanty   

adj.缺乏的，仅有的，节省的，狭小的，不够的

参考例句：

• There is scanty evidence to support their accusations.他们的指控证据不足。
• The rainfall was rather scanty this month.这个月的雨量不足。

21 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。