Part 10
(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.
(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) [Illustration]
(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) [Illustration]
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) [Illustration]
(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) [Illustration]
(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) [Illustration]
(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.