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. - John Scott

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.
(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. 11⅞ 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—

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

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

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.

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.

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

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

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

8	256	2
4	16	64
128	1	32