Chapter V: Part 5

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.

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)

(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
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)

(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)

(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)·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)

(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) 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)

(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) 4⅘lbs.

(201)

(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)

(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.

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

THE KNIGHT MOVE.

(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.

(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. 11⅞ in.

(251)

1st boy, 14·18 farthings
2nd " 3·82 "

(252)

Jack, 10 yrs. Tom =FIVE= Tom =F=ive
James, 9 " Bob =S=ix Bob =S=ix
Fred, 8 " Jack =T=en Fred =E=ight
Bob, 6 " Baby =O=ne Jack =T=en
Tom, 5 " James =N=ine Baby =O=ne
Baby, 1 " Fred =E=ight James =N=ine

(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)33/17(196078431372549

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) 1⅔ minutes.

(270) 49 years.

(271) 3 minutes.

(272)

| | | | |
-----------+----------+-----+-----+--
A B C D E

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 2_x_) 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_
∴ 1250-25_x_-_x_^2 eq. 25_x_ plus _x_^2
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.