Part 10

273. If eight men are engaged in a tug-o’-war, four pulling against four, on a continuous rope, and each man is exerting a force of 100 lbs., what strain is there at the centre of the rope?

“FIND OUT.”

274. A gentleman in a train with a boy got into conversation with a stranger, who asked him the lad’s age. The boy quickly replied, “This gentleman, who is my uncle, is twice as old as me, but the sum of the figures in my age are twice the sum of those in his.” What was the age of each?

275. One of our squatters who had made his fortune in the “good times” determined to sell his run and spend the rest of his days in the old country. A new chum, possessing considerable wealth, and desirous of settling down in Australia, hearing of the squatter’s intention, interviewed him with the object of purchasing, when the following conversation ensued:--

NEW CHUM: “How big is your run? What’s its area?”

SQUATTER: “Well, I’m blessed if I know, but I can tell you it’s perfectly square and enclosed with posts and rails. Each of the rails is 9 ft. long.”

NEW CHUM: “Oh, then, is it what you call a three-railed paddock?”

SQUATTER: “Yes, that’s so, and now I remember that _the number of rails in my run is equal to the number of acres_. If you like you can take a horse and ride round and count the rails, then you will know the area.” This advice the new chum acted upon.

Find out the length of his ride and the area of the run.

A Federal Problem.

It is well known to our readers that paper money--such as pound notes--issued in one colony are depreciated in another; thus a one pound note of N.S.W. is only worth 19s. 6d. in Victoria, and _vice versa_. Some time ago a rather ’cute individual in Wodonga, on the Victorian side of the border, bought a drink in a local hotel with a Victorian note, and received in change a N.S.W. note, which was worth then and there only 19s. 6d.; he thereupon crossed the Murray to Albury on the New South Wales side, bought another drink for sixpence with his N.S.W. note, and received a Victorian note equal to 19s. 6d. in change. He travelled backwards and forwards during the day, getting his twentieth and last drink in Albury, on the N.S.W. side, whereupon he returns to Wodonga with a Victorian pound note still to his credit. He thus paid for all his drinks, which amounted to ten shillings. Who lost the money?

We cannot advise readers to “go thou and do likewise,” for the simple reason that such a proceeding would now be impossible, as exchange is no longer charged in the two towns mentioned. It is not until we get further from the border that the levy is made.

Doing Two Things at Once.

An inspector was examining a school in a country district some distance from a railway station. He was afraid of losing his train, so hurrying with his work he tried to do two things at once. Standing in the doorway, he gave out dictation to Class III. in the main room, and at the same time gave out a sum to Class IV. in an adjoining room, jerking out a few words alternately.

The sum was “If a couple of fat ducks cost 19s., how many can he get for £72 10s. 9d.” The dictation for Class III. began “Now as a lion prowling about in search, &c.” Of course the poor children heard both, and got a bit mixed. One little girl’s dictation began “Now a couple of ducks prowling about in search of a lion who had lost 19s., &c.” While a Class IV. lad was scratching his head over the following sum “If 72 couples of fat lions cost 19s., how much prowling could be got for £72 10s. 9d.”

TWO CALENDAR CATCHES.

Ask a person if Christmas Day and New Year’s Day come in the same year. The answer generally given is “Of course not, Christmas comes in this year, and New Year’s Day in the next.”

Another question that often puzzles many. Have we had more Christmas days than Good Fridays? The usual answer is “No, both the same.”

276. A brass memorial tablet in honour of the late Sir Charles Lilley has been fixed in the centre of the eastern wall of the Brisbane Grammar School Hall. The enthusiasm displayed by Sir Charles in the cause of education generally, and his work on behalf of the Grammar School, make this commemoration particularly appropriate. The following is the inscription, to translate which should prove a capital exercise to all Latin scholars. The tablet measures 50 inches by 30 inches.

[Illustration: MEMORIAL TABLET TO THE LATE SIR CHARLES LILLEY]

It may be added that the lettering of the plate was designed by Mr. R. S. Dods, architect, and the engraving was done in Brisbane by Messrs. Randle Bros., the well-known engravers, of Elizabeth Street.

A Puzzle in Book-keeping.

277. A firm appointed an agent to do business on their account, and gave him £32 17s. in cash for expenses, &c., and also supplied him with a stock of goods, the value wholesale being £57 14s.; while in a distant town he bought a job lot of goods for £59 19s., which he paid cash for out of what he had realised on his first stock. He still continued to sell, but very soon after the firm called him in, and desired him to close his account and hand in a full statement.

His total retail sales amounted to £102 17s., and he returned goods to the value of £31 17s., his expenses had been £25.

Question--What does the firm owe the agent, or the agent owe the firm?

THE AGENT’S STATEMENT BEING--

Cash £32 17 Goods 57 14 Paid for Goods 59 19 Cash Sales 102 17 Goods Returned 31 17 Expenses 25 0

This puzzle first appeared in “HOW TO BECOME QUICK AT FIGURES,” the answer being withheld. It is a record of transactions that actually occurred in America, which were the subject of litigation. Although we received thousands of replies, not more than 5 per cent. were correct. It is a question that individuals not conversant with book-keeping would be as likely to solve correctly as the expert. For the convenience of those who are unacquainted with American money we have been obliged to substitute £ s. d., and would advise our readers to attempt a solution before referring to the answer.

CONCLUSION.

In bringing “THE PUZZLE KING” to a conclusion, the author can only express the hope that he has been successful in his endeavour to make it not only an amusing work but also a _useful_ one.

The impossibility of making a book of this nature perfect is fully recognised, and corrections or contributions will be cordially received, and the contributor liberally remunerated.

All communications must be sent to 44 Pitt Street, Sydney, addressed to the author, who tenders to all readers of “THE PUZZLE KING”--

AN ARITHMETICAL TOAST. “Here’s an _addition_ to your wages. Here’s a _subtraction_ from your wants and miseries. Here’s a _multiplication_ of your joys and happiness. Here’s a _division_ amongst your enemies. Here’s a _reduction_ of your hours of labour. And here’s a hope that you’ll all be able to _practice_ and take _interest_ in “THE PUZZLE KING.”

Answers.

(1) 12,111.

(2) 24s.

(3) 18.

(4) He lost £13 6s. 8d.

(5)

+-----+-----+-----+-----+ | 485 | 463 | 475 | 465 | +-----+-----+-----+-----+ | 461 | 467 | 487 | 473 | +-----+-----+-----+-----+ | 483 | 477 | 457 | 471 | +-----+-----+-----+-----+ | 459 | 481 | 469 | 479 | +-----+-----+-----+-----+

(6) See No. 225.

(7) £30.

(8) 675 springs.

(9) [Illustration]

(10)

Suppose a man and woman to marry, the man to have had a son by a former marriage (the gentleman who leaves the money); also the woman has a daughter by a former marriage. This son and daughter get married, and have a son. This is the scheme of kindred, and answers the conditions of the paradox.

(11) 4d. There were three of them--grandfather, father, and son.

(12) The total score was 240. The 1st player scored 30; the 2nd and 3rd, 24 each; the 4th, 5th, and 6th, 12 each; the 7th, 8th, 9th, and 10th, 30 each; and the 11th, 6.

(13) They tip the pail over horizontally; if any part of the bottom can be seen without spilling the milk it is not half full.

(14) In 9-68/78 days.

(15) The measurements given would not make a triangle.

(16) 6400 soldiers.

(17) [Illustration]

(18) The LEFT BOWER.

(19)

The first £15 " second 8 " third 10 " fourth 6 --- The man had £39

(20) The first boat 15 min. 45 secs., the second 16 min.

(21) 3 animals.

(22) A comma.

(23) 15 and 10.

(24) 21 and 54.

(25) 126.

(26) 72 persons.

(27) 20·7846 inches; 203·646 square inches.

(28) 11 plus 1·1 = 12·1 11 x 1·1 = 12·1

(29) Coach fare 3s.

(30) The distance from the ends of the least side on the largest and intermediate sides are respectively 211⅓ and 176 links.

(31) 60.

(32) T wins--distance 90 miles; walking pace--T 5 miles per hour, D 4.

(33)

+---+---+---+---+---+---+---+---+---+ | A | B | C | D | E | F | G | H | I | +---+---+---+---+---+---+---+---+---+

My friends,--I have spare blankets, and I shall need no more; The tenth man can have my bed, and I’ll sleep on the floor. In room marked A two men were placed; the third was lodged in B; The fourth to C was then assigned, the fifth retired to D; In E the sixth he tucked away, in F the seventh man, The eighth and ninth in G and H, and then to A he ran (Wherein the host, as I have said, had laid two travellers by); Then taking one--the tenth and last--he lodged him safe in I: Nine spare rooms--a room for each--were made to serve for ten. And this it is that puzzles me and many wiser men.

(34) £78 7s. 0·42d.

(35) 275625 leaves.

(36) [Illustration: _Fig 1_]

(37) 24000 men.

(38) 4032 lines.

(39) 28·9 miles.

(40) £26 7s. 7d.

(41) 7 and 1.

(42)

+----------------------------+ | 47 58 69 80 1 12 23 34 45 | | 57 68 79 9 11 22 33 44 46 | | 67 78 8 10 21 32 43 54 56 | | 77 7 18 20 31 42 53 55 66 | | 6 17 19 30 41 52 63 65 76 | | 16 27 29 40 51 62 64 75 5 | | 26 28 39 50 61 72 74 4 15 | | 36 38 49 60 71 73 3 14 25 | | 37 48 59 70 81 2 13 24 35 | +----------------------------+

(43)

8 3 4 1 5 9 6 7 2

(44) Don’t be A flat be A sharp.

(45) £49.

(46)

+-----------+ | 3 3 3 | | | | 3 3 | | | | 3 3 3 | +-----------+

+-----------+ | 4 1 4 | | | | 1 1 | | | | 4 1 4 | +-----------+

(47) Give the last person an egg on the dish.

(48) 20 lbs.

(49) 1 wether, 10 ewes, 9 lambs.

(50) 15 hours.

(51) 12 square miles.

(52) 7 persons.

(53) The versed sine of the segment of Will’s cake which was given to Jack was 3·05 inches, and its area 26·0058364375 square inches: hence Will’s share was 704·6125135625 square inches, and Jack’s share 704·5914364375 square inches; so that Will’s four were about 52·03275 square inches more than Jack’s six, and Will, of course, lost the wager. After the decision of the gauger, Will’s share was ·0210771245 (1-50th nearly) of a square inch more than Jack’s.

(54) 8·46851 seconds velocity, 129·38 ft. per second.

(55) 144 minutes.

(56)

39 12 ----- 78 39 ----- 468

(57) 8835 yds.

(58) 2513·28 sq. yds nearly.

(59) A 13 times, B 8.

(60) Her son.

(61) 3 wickets.

(62) Not fully stated--suppose 4 miles per hour.

(63) 22 plus 2 eq. 24; 3^3-3 eq. 24.

(64) 1s. 11d. or 11s. 1d.

(65) TOBACCO.

(66) 1 ft. 5·6268 inches.

(67) [Illustration]

(68) Age 28.

(69) 8/9

(70) [Illustration: 1 2 3 4 5 6 7 8 9 10]

4 on 1, 6 on 9, 8 on 3, 5 on 2, and 10 on 7.

(71) They put one plank across the angle; the end of the other resting on it will reach the island.

(72) 283; 224.

(73) 23; 24.

(74) Gallons 1207·45, diameter 6 ft., height 6 ft, 10¼ in.

(75) 76; 24.

(76) One travels West and the other East going round the world once a year; one will gain one day per annum, and the other will lose a day. In 50 years the difference will amount to 100 days.

(77) Diameter 87032 miles, circumference 273529 miles, area 23805775928 miles.

(78)

+-----+-----+-----+ | 621 | 642 | 627 | | | | | | 636 | 630 | 624 | | | | | | 633 | 618 | 639 | +-----+-----+-----+

(79) The two ends of the box are placed so that they lap over the two sides, and the wood being one inch thick the length is thus increased by 2 inches.

(80) 96s.

(81) First £25 5s., second £28 5s., third £30 5s., fourth £36 5s.

(82) [Illustration]

(83) (5-5/5)·5.

(84) 10 inches.

(85) 5 miles 1300 yds.

(86) £10.

(87) 10, 22, 26.

(88)

987654321 = 45 555555555 = 45 123456789 = 45 or 99999 = 45 --------- --------- 864197532 = 45 555455556 = 45

(89)

The 1st part 8 add 2 = 10 " 2nd " 12 subtract 2 = 10 " 3rd " 5 multiply by 2 = 10 " 4th " 20 divide by 2 = 10 ---- 45

(90)

3025. 30 plus 25 = 55 which squared is 3025 9801. 98 plus 01 = 99 which squared is 9801

(91) 3 children.

(92) 36 inches.

(93) The difficulty is to determine what would have been the will of the testator had he foreseen that his wife would be delivered of twins. As he desired that in case his wife brought forth a son he should have ⅔ of his property, and the mother ⅓, it follows that his intention was to give his son a sum double to that of the mother; and as he desired in the other case that if she brought forth a daughter the mother should have ⅔ and the daughter ⅓, there is reason to conclude that he intended the share of the mother to be double that of the daughter; consequently, to unite these two conditions, the heritage must be divided in such a manner that the son may have twice as much as the mother, and the mother twice as much as the daughter. Thus we get--

Son’s share, £4000 Mother’s " £2000 Daughter’s " £1000

Sometimes the following difficulty is proposed in regard to this problem:--In case the mother should have two sons and one daughter, in what manner must the property be divided then? We refer you to the lawyers.

(94) 23 years 289 days--a little less than 24 years.

(95) [Illustration]

(96) 1650 ft. deep; 1½ minutes.

(97) [Illustration]

(98)

Man, 69 yrs 12 weeks Woman, 30 yrs 40 weeks

(99) A 18 hours, B 22½.

(100) 3 and 2.

(101) 12 pence.

(102) 50s.

(103)

It is used so in the question. The answer generally given is found in the Bible (Judges xvi, 7 and 8). Samson was bound with “seven green withs.”

(104)

32 or 46 or 95-72/36 or 14 57 35 1-8/4 76 --- --------- 89 17 100 5 --- 1 98 3 --- 6 2 98 --- 4 100 2 --- --- 100 100

(105)

56 or 20 or 40 24 8 36 --- 80 7 15 1 35 7 9 46 98 3 19 2 --- --- 7 100 100 --- 100

(106) 44 feet.

(107) 8 persons.

(108) 8¼.

(109) The stone should fall into his hand.

(110) 6⅗ days.

(111) £5 8s. 6d.

(112) TEN

(113)

To explain this often causes much confusion. We must take a simple illustration: I have a garden containing 10 appletrees, all bearing fruit. Now, there are more trees than any tree has apples on it; there must be at least 2 trees having the same number of apples--for instance, if No. 1 tree has 1 apple, No. 2 has 2, and so on to No. 9; when we come to No. 10 tree, it must have the same as one of the other trees, as it could not have 10 or more according to our first supposition.

(114) It simply means that _four_ “nothings” equal _one_ “nothing.”

(115) He had a half-penny, and he borrowed a half-penny.

(116) 5.

(117) 30 apples.

(118) 18 and 27.

(119)

A 3240 B 2916 C 1944 D 2052 E 1728 Electors 6480.

(120)

A £12 B £20 C £30

(121) 45 miles.

(122) 80, 60, 45.

(123) £580.

(124) Hendrick and Anna. Claas and Catrün. Cornelius and Gertruig.

(125)

A 2304 B 1296

(126) £19,005.

(127) 15 days.

(128)

1st £2180 3s. 4¼d. 2nd £2380 15s. 11¼d. 3rd £2599 17s. 9¾d. 4th £2839 2s. 10¾d.

(129) 1-2/18 minutes.

(130) 36 pyramids.

(131) 82·076 feet.

(132) 55-5/5 = 56 = 4 x 4 plus 40.

(133) 6 women. 10⅞d. per yard.

(134) A 21. B 28. Youngest child 7.

(135)

We see that each of the members present paid 4d. to make up 5s. There must have been 15 persons present when the bill was paid, and consequently 18 at dinner. Now, it is evident that the classes are as 2, 3, and 4, making 4 Officers, 6 Non-com’s, and 8 Privates. Again, it is evident that 5s. being the sum to be paid by 1 Com. and 2 Non-coms.; each Com.’s share was 2s., and each Non-com’s 1s. 6d., and from the conditions of the question each Private’s share was 1s. 3d.; those who remained had to pay. 3 Officers, 2s. each and 4d. each 7s. 0d. 4 Non-coms, 1s. 6d. each " 7s. 4d. 8 Privates, 1s. 3d. " " 12s. 8d. ----------- Amount £1 7s. 0d.

(136) The Alphabet.

(137) 4 glasses.

(138) 37·6992 feet.

(139) 157-1/7 square miles.

(140) 324.

(141) Bottle 2¼d., cork ¼d.

(142) 1, 4, 16, and 64.

(143) 16 days.

(144) 7¼d., 4¾d.

(145) 1st, 64; 2nd, 48; 3rd, 36; 4th, 27 gals.

(146) 1st £24, 2nd £20, 3rd £8, 4th £28.

(147)

This is one of those _impossible_ questions that one often hears. The fractions, when added together, equal 19/20. So the whole £1 _cannot be so divided_. The following solution is often put forward:--

⅓ plus ¼ plus ⅕ plus ⅙ = 20 plus 15 plus 12 plus 10 = 57 -------------------------- -- 60 60 s. 20 x 20 = 400 div. 57 = 7-1/57 to 1st son 15 x 20 = 300 div. 57 = 5-15/57 " 2nd " 12 x 20 = 240 div. 57 = 4-12/57 " 3rd " 10 x 20 = 200 div. 57 = 3-29/57 " 4th " -------- 20s.

(148) The locomotive pushes No. 1 truck up to the points, then returns to the opposite siding and pushes No. 2 up to No. 1 at the points; the two trucks are then pulled by the locomotive down the siding and pushed on to the main line to a position anywhere between the two sidings; No. 1 is then uncoupled and left standing, whilst the locomotive pulls No. 2 along the main line in order to push it up to the points where it is left; the locomotive returns to No. 1, and pulling it a short distance, in order to get on the proper siding, pushes it into its required position, uncouples, and proceeds up the other siding to the points to pull No. 2 into its proper place, then uncouples and returns to the main line.

(149) 14,400 quarts

(150) A, 2s. 7½d.; B, 1s. 1½d.; C, 9d.

(151)

1st Company, £2400 2nd " 1800 3rd " 1600 4th " 1500 ----- £7300

(152) Lines, 29; letters, 32.

(153) Major £100, minor £60.

(154) From A £88, from B £44.

(155) [Illustration]

(156) 25 miles from Sydney.

(157) 4½ miles.

(158) 108.

(159)

Two-thirds of SIX is IX; the upper half of XII is VII; The half of FIVE is IV; and the upper half of XI is VI.

(160) £12 12s. 8d. = 12128 farthings.

(161) J £660, M £440, B £220.

(162) Masons 20s., Bricklayers 15s., Laborers 10s.

(163) £29 19s. 9¼d.

(164) 2 years.

(165) [Illustration]

This draught puzzle can also be done in three other ways.

(166)

Wife £4650 Son 6200 Eldest daughter 3100 Youngest " 1550 ------ Total £15,500

(167) [Illustration]

(168) 18.

(169) 6¼ per cent.

(170) 19 movements 19 feet

(171) 895 and 11,277.

(172) 56 quarts.

(173) 20; 50 gals.

(174) 117 ft. 9 in.

(175) 1st 1¼d., 2nd ¾d.

(176)

The lazy sundowner 2 days at 2 hours per day = 4 hours " second " 4 " " 4 " " " = 16 " " third " 6 " " 6 " " " = 36 " " fourth " 12 " " 12 " " " = 144 " -------- 200 hours

(177) 17777873.

(178) The “catch” is in the word _ears_; he carries out two ears on his head and one ear of corn each day--hence it will take 6 days.

(179) My daughter.

(180) Man 3s., boy 2s.

(181) 11·9.

(182) 72 gals.

(183) The landlord would lose by such an arrangement, as the rent would entitle him to 2/5 of the 18; the selector should give him 18 bushels from his own share after the division is completed.

(184) £1 6s. 8d., £1 13s. 4d.

(185) 3.362 inches.

(186) The merchant, 1d.

(187)

Train from London 44 miles per hour " " Edinburgh 53-7/9 " " "

(188) A gentleman and one servant go over; the gentleman returns with the boat, 2 servants go over; 1 servant returns; 2 gentlemen go over; 1 gentleman and 1 servant return; 2 gentlemen go over; 1 servant returns; 2 servants go over; 1 servant returns; the two servants then go over.

(189)

Imperfect. (Sample of questions we receive daily. Give it to your friends: it will annoy them.)

(190) 14, 112, 378, 896.

(191) 120 lbs.

(192) 80 years.

(193) 6-6/6.

(194) 13 trains.

(195) Distance, 12½ miles; rate, 8 miles per hour.

(196) 5½ hours.

(197) A 39s., B 21s., C 12s.

(198) £10.

(199) When Pharaoh’s daughter drew a little prophet (profit) from the banks of the Nile.

(200) 4⅘lbs.

(201) [Illustration]

(202) 30 oz. of 21, 90 oz. of 23.

(203) £1 2s. 2⅔d.

(204) 3078 ac. 3r. 2·88p.

(205) 108 trees.

(206) 792.

(207) [Illustration]

(208) 8/50.

(209) 72 inches.

(210) 99-9/9.

(211) A 5, B 7.

THE BRICK PUZZLE.

(212) 2 stretchers, 4 headers, 4 closures. Area, 135 inches.

This question has been the cause of much discussion, especially amongst those engaged in the building trade.

[Illustration: Fig. 1--Represents the brick and the method of cutting it.]

[Illustration: Fig. 2--Represents the face of the wall showing the area of brick when cut. It has been necessary to produce this figure on half-scale to that of Fig. 1.]

(213) Goose 30, duck 50, hen 70.

THE KNIGHT MOVE.