The Puzzle King / Amusing arithmetic, book-keeping blunders, commercial comicalities, curious "catches", peculiar problems, perplexing paradoxes, quaint questions, queer quibbles, school stories, interesting items, tricks with figures, cards, draughts, dice, dominoes, etc., etc., etc.

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)

_
(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)

_
(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 211? and 176 links.
(31) 60.
(32) T wins—distance 90 miles; walking pace—T 5 miles per hour, D 4.
(33)

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)

_
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)

_
(44) Don’t be A flat be A sharp.
(45) £49.
(46)

_
(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; 3³ - 3 eq. 24.
(64) 1s. 11d. or 11s. 1d.
(65) TOBACCO.
(66) 1 ft. 5·6268 inches.
(67)

_
(68) Age 28.
(69) ⁸/₉
(70)

_
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)

_
(83) ( ⁵/₅)·5.
(84) 10 inches.
(85) 5 miles 1300 yds.
(86) £10.
(87) 10, 22, 26.
(88)

987654321 = 45 or 555555555 = 45

123456789 = 45 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 ? of his property, and the mother ?, 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 ? and the daughter ?, 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)

_
(96) 1650 ft. deep; 1½ minutes.
(97)

_
(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) 6? 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. 10?d. 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:—
? plus ¼ plus ? plus ? = 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)

_
(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)

_
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)

_
(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) 4?lbs.
(201)

_
(202) 30 oz. of 21, 90 oz. of 23.
(203) £1 2s. 2?d.
(204) 3078 ac. 3r. 2·88p.
(205) 108 trees.
(206) 792.
(207)

_
(208) ⁸/₅₀.
(209) 72 inches.
(210) 99 ⁹/₉.
(211) A 5, B 7.
(212) The Brick Puzzle.
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.
_
Fig. 1—Represents the brick and the method of cutting it.

_
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.
(214) It does not matter on which square the knight is first placed, his last square to enter will be at a knight’s distance from the first. The route may be varied in many ways.

The Knight Move.
_
(215) 2.
(216) A £3, B £6, C £18.
(217) Cannot be answered.
(218)

8 256 2

4 16 64

128 1 32
(219)

Even, £6 against £6— £12

2 to 1, £8 against £4— £12

3 to 1, £9 against £3— £12

£13 Received.
Whichever horse wins, he must pay £12, and has received £13 to pay with.
(220) 8.
(221) 9 to 8 on.
(222) 1 lb. of feathers by 1240 grains; 1 oz. of gold by 42·5 grains.
(223)

_
(224) Sovereigns, 4; half-crowns, 8.
(225) Count backwards, saying 20, 19, 18, 17, with emphasis on the 17, remarking “That’s odd, isn’t it?” The reply will be “Yes.” Proceed in that manner throughout. This question and No. 6, although not the best of “catches,” are often asked.
(226)

SIX IX XL

IX X L

——————

S I X
(227) Man 24, woman 16.
(228) 72 miles.
(229) The diameter of the earth.
(230) £420.
(231) ·000011574.
(232) 18 seconds.
(233) 19·405 inches.
(234)

_
He must cut the piece of veneer as
shown by the middle figure, when he
will be able to get his two ovals.
(235) Because you double it when you put it in your pocket, and you see it in creases (increases) when you take it out.
(236) He did this in two ways;—

Table Full. Half-full. Empty.

1 " 2 3 2

2 " 2 3 2

3 " 3 1 3

1 " 3 1 3

2 " 3 1 3

3 " 1 5 1
(242)

_
(243)
7
7 6 7
5
4
3
2
1
(244) 180.
(245) Worked 27 days, idle 33.
(246) XIX, take away I, leaves XX.
(247) The Cadi added his camel to the 17, thus making 18 in all; then the oldest son received 9, second son 6, youngest 2. He then took his own camel, and, departing, left the sons quite satisfied.
(248) 2, 4, 8, 16, 32, 64 lbs.
(249) 13 horses, 26 cattle, 39 pigs.
(250) 12 ft. 11? in.
(251) 1st boy, 14·18 farthings
2nd " 3·82 "
(252)

Jack, 10 yrs. Tom FIVE Tom Five

James, 9 " Bob Six Bob Six

Fred, 8 " Jack Ten Fred Eight

Bob, 6 " Baby One Jack Ten

Tom, 5 " James Nine Baby One

Baby, 1 " Fred Eight James Nine
(253) 79·26 feet.
(254) 9 plus 9 plus 9 plus 3 = 30, 39 ⁹/₉ = 40, or 28 ²/₁ = 30, 28 plus 12 = 40.
(255) 5d.
(256) 196078431372549.
Method: Keep on adding imaginary 3’s until it comes out thus—

17)	33	(196078431372549
	17

To prove it:—	196078431372549
	17
Proof—	3333333333333333

(257)

28 eggs. Method: 1½ hens lay 1½ eggs in 1½ days

1½ " " 3 " " 3 "

3 " " 6 " " 3 "

3 " " 2 " " 1 "

6 " " 4 " " 1 "

6 " " 28 " " 7 "
(258) Tom, 4s. 6d. per day; Bill, 3s.
(259) 1000.
(260) 1 inch remainder.
(261)

_
(262) 393,213 shillings.
(263) ²/₉.
(264) 9½.
(265) 4 seconds.
(266) Loses £50.
(267) He will never enter the water, because the frog’s jump, at any time, is only half-way to the water.
(268)

_
(269) 1? minutes.
(270) 49 years.
(271) 3 minutes.
(272)

_
Let A be starting point of Orderly; B be starting point of General; C be point at which Orderly returns to his place, the rear having marched 50 miles to this point; D be point at which Orderly delivers his despatches; E be destination of front rank or General of Army.
Let x eq. number of miles between C and D.
Then AD eq. (50 plus x) miles; BD eq. (25 plus x) miles; DE eq. (25 minus x) miles; and AD plus DC eq. (50 plus 2x) miles, and is the total distance the Orderly travels.
Now Orderly rides from A to D, while General marches from B to D, and Orderly returns from D to C, while General marches from D to E, and Orderly and Army travel at a uniform rate.
? AD : BD :: DC : DE
or 50 plus x : 25 plus x :: x : 25 - x
? 1250 - 25x - x² eq. 25x plus x²
Whence x eq. 15.45 plus.
? Orderly rides 50 plus 30.9 plus
eq. 80.9 plus
eq. 80 miles 1587 yards nearly.
(273) 400 lbs.
(274) Gentleman 30, boy 15.
(275) Ride, 44 miles; area, 77,440 acres.
(276) Translation: The foundation stone of this building was laid in 1880 by Sir Charles Lilley, for many years Chief Justice, and formerly a distinguished member of the Government of this colony. He was prominent amongst those who worked for the first establishment of this school, and afterwards, by his generous gifts and by his wise counsel as a trustee, contributed greatly to its advancement. The trustees have, therefore, erected this tablet to perpetuate his memory here. A.D. 1898.
(277) The agent owes the firm £7 19s.

DIDDAMS PRINTER, BRISBANE.

Transcriber's Notes:

The cover image was created by the transcriber and is placed in the public domain.

Antiquated spellings have been preserved.

Typographical errors have been silently corrected but other variations in spelling and punctuation remain unaltered.

Answers are provided at the end of the book to numbered questions, however in the original text, numbers 237 to 241 were omitted for some reason.

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