Chapter V: Hand Shadows and how to work them. Illustrated (7)

107. What would it cost me to keep my word if I were to offer my greengrocer a farthing for every different group of ten apples he could select from a basket of a hundred apples?

108. If the minute-hand of a clock moves round _in the opposite direction_ to the hour-hand, what will be the real time between three and four, when the hands are exactly together?

109. Two monkeys have stolen some filberts and some walnuts. As they begin their feast they see the owner of the garden coming with a stick. It will take him two and a half minutes to reach them. There are twice as many filberts as walnuts, and one monkey finishes the walnuts at the rate of fifteen a minute in four-fifths of the time and bolts. The other manages to finish the filberts just in time.

If the walnut monkey had stopped to help him till all was finished, when would they have got away if they ate filberts at equal rates?

110. A cashier, in payment for a cheque, gives by mistake pounds for shillings and shillings for pounds. The receiver spends half-a-crown, and then finds that he has twice as much as the cheque was worth. What was its value?

111. What five uneven figures can be added together so as to make up 14?

112. Three posts which vary in value are vacant in an office. In how many ways can the manager fill these up from seven clerks who apply for the appointments?

113. “It is now ⁵⁄₁₁ of the time to midnight,” said the fasting man, who began his task at noon. What time was it?

A STRIKING TIME

114. If a clock takes six seconds to strike six how long will it take to strike eleven?

WHAT ARE THE ODDS?

115. How would you arrange twenty horses in three stalls so as to have an odd number of horses in each stall?

116. Here is a pretty little problem, which has at any rate an Algebraic form, and is exceedingly ingenious:--

Given _a_, _b_, _c_, to find _q_.

WHEN WAS HE BORN?

117. Tom Evergreen was asked his age by some men at his club on his birthday in 1875. “The number of months,” he said, “that I have lived are exactly half as many as the number which denotes the year in which I was born.” How old was he?

118. Draw three circles of any size, and in any position, so long as they do not intersect, or lie one within another. How many different circles can be drawn touching all the three?

119. We have seen that the nine digits can be so dealt with, using each once, as to add up to 100. How can 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 be arranged so that they form a sum which is equal to 1?

120. How is it possible, by quite a simple method, to find the sum of the first fifty numbers without actually adding them together?

121. Two tram-cars, _A_ and _B_, start at the same time. _A_ runs into a “lie by” in four minutes, and waits there five minutes, when _B_ meets and passes it. Both complete the whole course at the same moment. In what time can _A_ complete it without a rest?

A CURIOUS DEDUCTION

122. Take 10, double it, deduct 10, and tell me what remains.

123. The average weight of the Oxford crew is increased by 2 lbs., when one of them, who weighs 12 stone, is replaced by a fresh man. What is the fresh man’s weight?

ASK ANY MOTORIST

124. A motor car is twice as old as its tyres were when it was as old as its tyres are. When these tyres are as old as the car is now, the united ages of car and tyres will be two years and a quarter. What are their respective ages now?

125. _A_ and _B_ on the edge of a desert can each carry provisions for himself for twelve days. How far into the desert can an advance be made, so that neither of them misses a day’s food?

126. A bottle of medicine and its cork cost half-a-crown, but the bottle and the medicine cost two shillings and a penny more than the cork. What did the cork cost?

IN A FIX

127. A boat’s crew are afloat far from land with no sail or oars. How can they, without making any use of wind or stream, and without any outside help, regain the shore by means of a coil of rope which happens to be at hand.

128. What is the largest sum in silver that I can have in my pockets without being able to give change for a half-sovereign.

129. I have apples in a basket. Without cutting an apple I give half of the number and half an apple to one person; half of what then remains and half an apple to another, and half of what are still left and half an apple to a third. One apple now remains in the basket. How many were there at first?

A QUEER DIVISION

130. A third of twelve divide
By just a fifth of seven;
And you will soon decide
That this must give eleven.

131. A motor goes 9 miles an hour uphill, 18 miles an hour downhill, and 12 miles an hour on the level. How long will it take to run 50 miles and return at once over the same course?

132. In firing at a mark _A_ hits it in two out of three shots, _B_ in three out of four, and _C_ in four out of five. The mark was hit 931 times. If each fired the same number of shots, how many hits did each make, and how many shots were fired?

133. If a cat and a dog, evenly matched in speed, run a race out and back over a course 75 yards in all, and the dog always takes 5 feet at a bound and the cat 3 feet, which will win?

IN A FOG

134. In a fog a man caught up a wagon going in the same direction at 3 miles an hour. If the wagon was just visible to him at a distance of 55 yards, and he could see it for five minutes, at how many miles an hour was he walking?

135. Three horses start in a race. In how many different ways can they be placed by the judge?

NEW ZEALAND FOOTBALL

136. The New Zealanders, winning a match against Oxbridge, scored 34 points, from tries and tries converted into goals.

If every try had been converted they would have made four-fifths of the maximum which a score of 34 points from tries and goals can yield.

What is this maximum, and what was their actual score?

137. What is the smallest number, of which the alternate figures are cyphers, that is divisible by 9 and by 11?

138. Here is an interesting little problem:--_A_, with 8d. in his hand, meets _B_ and _C_, who have five and three loaves respectively. In hungry mood they all agree to share the loaves equally, and to divide the money fairly between _B_ and _C_. How much does each receive?

THE MONEY-BOXES

139. When four money-boxes, containing pennies only, were opened and counted, it was found that the number in the first with half those in all the others, in the second with a third of all the others, in the third with a fourth of all the others, and in the fourth with a fifth of all the others, amounted in each case to 740. How much money did the boxes contain, and how was it divided?

140. Two steamers start together to make a trip to a far-off buoy and back. Steamer _A_ runs all the time at 10 miles an hour. Steamer _B_ does the passage out at 8 miles an hour, and the return at 12 miles. Will they regain port together?

141. A golf player has two clubs mended in London. One has a new head, the other a new leather face. The head costs four times as much as the face. At St Andrews it costs five times as much, and the leather face at St Andrews is half the London price. Including a shilling for a ball he pays twice the St Andrews charges for these repairs. What is the London charge for each?

FROM TWO WRONGS TO MAKE A RIGHT

142. Two children were asked to give the total number of animals in a pasture, where sheep and cattle were grazing. They were told the numbers of sheep and of cattle, but one subtracted, and gave 100 as the answer, and the other arrived at 11,900 by multiplication. What was the correct total?

THE STONE CARRIER

143. Fifty-two stones are placed at intervals along a straight road. The distance between the first and the second is 1 yard, between the second and the third it is 3 yards, between the next two 5 yards, and so on, the intervals increasing each time by 2 yards.

How far would a tramp have to travel to earn five shillings promised to him when he had brought them one by one to a basket placed at the first stone?

144. On a division in the House of Commons, if the Ayes had been increased by fifty from the Noes, the motion would have been carried by five to three. If the Noes had received sixty votes from the Ayes, it would have been lost by four to three. Did the motion succeed? How many voted?

A WATCH PUZZLE

145. How many positions are there on the face of a watch in which the places of the hour and minute-hands can be interchanged so as still to indicate a possible time?

CRICKET SCORES

146. In a cricket match the scores in each successive innings are a quarter less than in the preceding innings. The match was played out, and the side that went in first won by fifty runs. What was the complete score?

HOW HIGH CAN YOU THROW?

147. A boy throws a cricket ball vertically upwards, and catches it as it falls just five seconds later. How high from his hands does the ball go?

MEASURE THE CARPET

148. It may be said of a section of the gigantic carpet at Olympia that had it been 5 feet broader and 4 feet longer it would have contained 116 more feet; but if 4 feet broader and 5 longer the increase would have been but 113 feet. What were its actual breadth and length?

149. In estimating the cost of a hundred similar articles, the mistake was made of reading pounds for shillings and shillings for pence in each case, and under these conditions the estimated cost was £212 18s. 4d. in excess of the real cost. What was the true cost of the articles?

SQUARES IN STREETS

150. The square of the number of my house is equal to the difference of the squares of the numbers of my next door neighbour’s houses on either side.

My brother, who lives in the next street, can say the same of the number of his house, though his number is not the same as mine. How are our houses numbered?

151. Two men of unequal strength are set to move a block of marble which weighs 270 lbs., using for the purpose a light plank 6 feet long. The stronger man can carry 180 lbs. How must the block be placed so as to allow him just that share of the weight?

152. A man has twenty coins, of which some are shillings and the rest half-crowns. If he were to change the half-crowns for sixpences and the shillings for pence he would have 156 coins. How many shillings has he?

COUNT THE COINS

153. Some coins are placed at equal distances apart on a table, so that they form the sides of an equilateral triangle.

From the middle of each side as many are then taken as equal the square root of the number on that side, and placed on the opposite corner coin. The number of coins on each side is then to the original number as 5 is to 4. How many coins are there in all?

PUTTING IN THE POSTS

154. A gardener, wishing to fence round a piece of ground with some light posts, found that if he set them a foot apart there would be 150 too few, but if placed a yard apart there would be 70 to spare. How many posts had he?

155. _A_ gives _B_ £100 to buy 100 animals, which must be cows at £5 each, sheep at £1, and geese at 1s. How many of each sort can he buy?

156. John is twice as old as Mary was when he was as old as Mary is. John is now twenty-one. How old is Mary?

157. In a cricket match _A_ made 35 runs; _C_ and _D_ made respectively half and one-third as many as _B_, and _B_’s score was as much below _A_’s as _C_’s was above _D_’s. What did _B_, _C_, and _D_ each score?

SETTLED BY REMAINDERS

158. What is the least number which, divided by 2, 3, 4, 5, 6, 7, 8, 9, or 10, leaves respectively as remainders 1, 2, 3, 4, 5, 6, 7, 8, and 9?

TABLE TURNING

159. A square table stands on four legs, which are set at the middle point of its sides. What is the greatest weight that this table can uphold upon one of its corners?

BRIBING THE BOYS

160. Well pleased with the inspector’s report, the rector of a country parish came into his school with 99 new pennies in his pocket, and said that he would give them to the five boys in Standard VII. if they could, within an hour, show him how to divide them so that the first share should exceed the second by 3, be less than the third by 10, be greater than the fourth by 9, and less than the fifth by 16. What was the answer which would satisfy these conditions?

SHEEP-STEALING

161. Some Indian raiders carried off a third of a flock of sheep, and a third of a sheep. Another party took a fourth of what remained, and a fourth of a sheep. Others took a fifth of the rest and three-fifths of a sheep. What was the number of the full flock, if there were then 409 left?

162. Three boys begin to fill a cistern. _A_ brings a pint at the end of every three minutes, _B_ a quart every five minutes, and _C_ a gallon every seven minutes. If the cistern holds fifty-three gallons, in what time will it be filled, and who will pour in the last contribution?

ESTIMATE OF AGE

163. A man late in the last century said that his age was the square root of the year in which he was born. In what year did he say this?

A DEAL IN CHINA

164. A dealer in Eastern curios sold a Satzuma vase for £119, and on calculation found that the number which expressed his profit per cent. expressed also the cost price in pounds of the vase. What was this number?

165. What is the chance of throwing at least one ace in a single throw with a pair of dice?

166. A thief starts running from a country house as fast as he can. Four minutes later a policeman starts in pursuit. If both run straight along the road, and the policeman gets over the ground one-third faster than the thief, how soon will he catch him?

167. Twenty-seven articles are exposed for sale on one of the stalls of a bazaar. What choice has a purchaser?

VERY PERSONAL

168. “How old are _you_, dad?” said Nellie on her birthday, as her father gave her as many shillings as she was years old. His answer was quite a puzzle for a time, but with the help of her schoolfellows Nellie worked it out.

This is what he said:--

“I was twice as old as you are
The day that you were born.
You will be just what I was then
When fourteen years are gone.”

How old was Nellie, and how old was her dad?

WORD AND LETTER PUZZLES

A MAGIC COCOON

This Magic Cocoon is so cleverly spun that the word can be traced and read in many ways.

N
N O N
N O O O N
N O O C O O N
N O O C O C O O N
N O O C O C O C O O N
N O O C O C O O N
N O O C O O N
N O O O N
N O N
N

How many readings can you discover starting from one or other of the Cs, and passing up and down or sideways, but not diagonally, and never over the same letter twice in a reading? There are 756!

THE CHRONOGRAM

The Chronogram, severely classed by Addison as “a species of false wit” is a sentence in which the salient letters represent in Roman numerals some particular year. A good English specimen is this: “My Day Closed Is In Immortality.” The capital letters in these words give MDCIII., or 1603, the year in which Queen Elizabeth died.

A FRENCH CHRONOGRAM

The battle-cry at Montlhéry in 1465 was:--“à CheVaL, à CheVaL, gendarMes, à CheVaL!” Taking the letters printed in capitals--

M = 1000
CCC = 300
LLL = 150
VVV = 15
----
we have the date of the battle 1465

A NOTABLE CHRONOGRAM

QVI CHRISTI IAVDES CANTANT
SANCTÆ PASSIONIS SVÆ VIRTVTE
IN IPSO ET PATRE VNVM SINT.

This curious inscription is placed over the organ at Ober Ammergau. Add together its Roman numerals and they give the date at which the organ was dedicated. The English of it is:--

May those who sing the praises of Christ be by virtue of His Sacred Passion one in The Father and in Himself.

A PERFECT CHRONOGRAM

On a damaged inscription to Bishop Berkeley in Winchester Cathedral are the words--VIXI, LVXI--I have lived, I have shone. Added together in their values as Roman numerals the letters of these two words give his age exactly at his death--eighty-three.

A PRIZE MOTTO

On the return of the C.I.V. from the Boer War a prize was offered by _Truth_ for the best motto appropriate to them. This was to consist of three words of which the first must begin with C the second with I and the third with V.

The prize was taken by the following Latin motto which is singularly happy both in construction and in meaning:--

CIVI IVI VICI
_I roused_ _I went_ _I won._

The sequence of events is perfect; no letters but C.I.V. are used and the motto is a palindrome if read by syllables.

THE MUSICAL SCALE

As in olden days some of the Psalms and other writings were constructed in acrostic form, so in the Middle Ages even serious writers would juggle with letters, as though they felt that such tricky methods were an aid to memory.

It was in this spirit that Guido Aretino, a Benedictine monk of Tuscany in 1204, gave names to the notes used in the musical scale from the first syllables of the lines of a Latin hymn. “Ut” is still used in France, though we and the Italians have substituted “do.”

UT queant laxis REsonare fibris,
MIra gestorum FAmuli tuorum,
SOLve polutis LAbii reatis
O Pater alme!

ALL THE ALPHABET!

Many of us know that there is a long verse in the Book of Ezra in which all the letters of the alphabet are used, taking “j” as “i” (_Ezra_ vii., v. 21).

This very curious coincidence also occurs in a comparatively short sentence in “The Beth Book,” by Sarah Grand:--“It was an exquisitely deep blue just then, with filmy white clouds drawn up over it like gauze;” and here “j” is itself in evidence.

APT ALLITERATION

Schopenhauer, the famous German philosopher, who was a confirmed bachelor and misogynist, was compelled while living at Frankfort to support an old lady who had been crippled by his violence. When her death came as a welcome relief to him, he composed the following clever epitaph:--

Obit anus,
Abit onus.

which by the interchange of two letters pictured the position. It may be freely rendered:--

Old lady dies,
My burden flies.

A DOUBLE SEQUENCE

The following clever composition, which appeared in the pages of _Truth_, contains a _double_ sequence of words, which increase a letter at a time, the same letters appearing in varied order until at last “o” culminates in _thornless_, and “a” in _restrainest_. It is quite a remarkable _tour-de-force_.

O lack-_a_-day! _at_ eve we _sat_,
One _star_ had lit its lamps _on_ high.
We did _not note_ the circling bat,
_Start_ from the _stone_ when flitting nigh.
For the _strait_ gate of _honest_ doubt
Shut off the _thrones_ of Love and Gain;
We dreamed not, as we mourned without,
That Time’s swift _transit shortens_ pain.
O Thou, Who _trainest_ souls to shine,
Though once we craved a _thornless_ lot,
This gracious truth we now divine:
The bruised reed Thou _strainest_ not;
But by _restraints_, that gently tame;
_Restrainest_ Passion’s kindling flame.

THE REIGN OF TERROR

During the Reign of Terror, France and her people and position were thus alphabetically described:--

Le peuple Français A B C. (abaissé).
La gloire nationale F A C. (effacée).
Les places fortes O Q P. (occupées).
Quarante trois députés C D. (cédés).
L’armée D P C. (dépaysée).
Les ministres A J. (agés).
La liberté O T. (ôtée).
La charte L U D. (éludée).

SEE-SAW

This elaborate method of piling up no less than seven consecutive “thats,” so that they make tolerable sense, was told to his boys during school-time by Dr Moberly, then headmaster of Winchester, and afterwards Bishop of Salisbury, just fifty years ago:--

I saw that C saw.

C saw that that I saw.

I saw that that that C saw was so.

C saw that, that that that I saw was so.

I saw that, that _that_ that that C saw was so.

C saw _that_ that, that _that_ that that I saw was so.

I saw _that_ that, that _that_ that that _that_ C saw was so.

FOR A ROMAN HOLIDAY

If the Roman ladies and children, at their equivalent for Christmas, amused themselves by acting verbal charades, an excellent word was at their disposal, “sustineamus”--“let us endure,” which can be broken up exactly into _sus_, _tinea_, _mus_--_a sow_, _a moth_, _a mouse_.

A WORD SQUARE

1. Can you complete this word square, so that its four words read alike from top to bottom and from left to right?

* E * *
E * * *
* * * E
* * E *

ANOTHER WORD SQUARE

2. Can you fill in this word square?

C * * C * E
* N U * E S
* U * E S *
C * E * S *
* E S * * E
E * T E * *

DUPLICATE LETTERS

3. In this sentence, when complete,

So****AG****LATI****X****ITH

each group of four missing letters contains two pairs of letters which are alike. Can you on these lines complete the sentence?

Here is a similar sentence by way of illustration:

T****M****TERTAIN****MUND,

which becomes when filled in--

T_wo_ _wo_m_en_ _en_tertain_ed_ _Ed_mund.

ANOTHER WORD SQUARE

4. Can you complete this word square by substituting letters for the dots?

W * * * E
* * T * *
* T O N *
* * N * *
E * * * T

WORD BUILDING

5. What word can be made with these?

L S D U D O D U D.

6. A lovelorn youth consulted a married lady on his condition, and was asked by her on a slip of paper:--

“Loruve?”

When he had deciphered this, and had answered in the affirmative, she handed to him another slip, on which this advice was written:--

L
“Prove A F and ensure success.”
D

What did it all mean?

A DOUBLE ACROSTIC

7. _Saint of Spain, whose daily word
Twenty years hath London heard!_
Sweet days, elastic metal, motion sharp.
My halls once echoed to an Irish harp.
The “son of sorrow,” honourable of yore.
Dread goddess, loosing the loud dogs of war.
Time’s atom--total of eternities.
This name an insect bears, a patriot bore.
“So do, yet hear me,” said Themistocles.

ANOTHER WORD SQUARE

8. Can you complete this word square?

* M * N * S
M * N * O *
* N * B * E
N * B * L *
* O * L * R
S * E * R *

A FRENCH ORACLE

9. A spruce young Frenchman at a _fête_ consulted a modern oracle as to how he could best please the ladies. This was the mystic response:--

MEC DO BIC.

Can you interpret it?

A QUAINT EQUATION

10. In our young days we have often wrestled with vulgar fractions, but apart from Algebra we have had no serious concern with any in which letters take the place of figures. A specimen of this sort, not known to science, is the following curiosity:--

m
--
ot
-- = mo.
y

11. The puzzle in _Truth_ was recently founded upon “ourang-outang,” which had been cleverly buried. We will give a few of the best results. This is one:--

Poor wretch! a moisture filled his eye,
“Do not rebuff a lonely boy,”
Said he, “If ere I sink and die
Your smile--O! pardon will be joy!”

Another is:--

Though I jump, and row, and run,
Cap or cup I never won.

What animals are buried in these lines?

LIKE A PEACOCK’S TAIL

12. Fourteen letters here we fix,
Vowels only two are spoken;
All together these we mix
Into what can not be broken.

A WEIRD WORD

13. There is an English word of thirteen letters in which the same vowel occurs four times, the same consonant six times, another consonant twice, and another once. Can you hit upon it?

A CONDENSED PROVERB

14. Though brevity is said to be the soul of wit, we are too often flooded nowadays with a superabundance of words.

Here is an attempt at modest condensation. A familiar English proverb is quite clearly expressed to the solver’s seeing eyes in this brief phrase:--

WE IS DO

What is the proverb?

ANOTHER WORD SQUARE

15. Can you complete this word square?

W * * * * S
* R * * R *
* * O R * *
* * R M * *
* R * * N *
S * * * * M

CAN YOU DECIPHER IT?

16. The following puzzle lines are attributed to Dr Whewell:--

O O N O O.
-----------
U O A O O I O U
O N O O O O M E T O O.
U O A O I D O S O
I O N O O I O U T O O!

A BROKEN DIAMOND

17. Can you fill in the vacancies in this diamond?

P
F O *
C * R * *
F * * C * * *
P O R C E L A I N
R * * L * * *
S * A * *
S I *
N

Its words must read alike from left to right and from top to bottom.

WHAT IS THIS?

18. Tan HE Edsa VEN in
It N Gja SmeTs AsgN
aD Az Rett De.

A PHONETIC JOURNEY

19. I can travel first-class on the Great Eastern Railway from 2 2 2 2 2 2 2 2 4 4 4 4 4 5 0 0. What is the cost of my journey, and its length in time?

A CURIOUS OLD INSCRIPTION

20. Seogeh sreve ereh wcisume vahl
Lah sehs se otreh nos llebdnas
Regni freh nos gnires rohyer
Ganoed iryd ale nifae esots sorcy
Rub nabot es rohk co caed ir.

Can you decipher it?

IRISH STEW AT SIMPSON’S

21. I wrote the following note recently:--

Dear Jack,--Meet me at Simpson’s to-morrow at 1.30. We will sample
their excellent Irish stew. Here are some catchwords that will remind
you of the invitation:--

Join me at and
i
s

Why should they remind him of it?

ENGLISH AS SHE IS SPELT!

22. This was the exact text of a letter sent to the master of an English village school by a labourer as an excuse for his boy’s absence:--

“Cepatomtogoatatrin”

Can you decipher it?

A DOUBLE ACROSTIC

23. This double Acrostic will afford an easy exercise in mental gymnastics for those to whom such pastime appeals:--

Now we are fain
To rack your brain.

1. More fit for babes and sucklings than for you.

2. Robbed of externals this is very true.

3. Diminutive in measure and in weight.

4. Pen-name of one a true pen potentate.

5. A palindrome quite plain is here in sight.

6. Sans head and tail it also yields this light.

7. Here is in short what anyone may write.

FIND THE PROVERB

24. c e f h i m n o r s t v y
3 2 2 2 7 1 1 2 6 5 8 3 9
4 4 1 2 1 6 1
3 1 5 8 2 3
5 7 9 6
4

The letters with ones under them are the first letters of words, those with twos under them are second letters of words, and so on.

A PUZZLE WILL

25. Having occasion to make a few slight additions to my will, I called in my lawyer to arrange the matter. How far forward did the instructions contained in the following lines carry him in his work?

Set down a hundred in my will,
Add nothing to the text;
Five hundred now a space may fill,
And one be added next.

Another hundred write as well,
And yet another one;
Then fifty more, and try to tell
The deed that now is done.

ANOTHER WORD SQUARE

26. Can you complete this word square?

* D * * O *
D * * I * E
* S * A * D
T * A * A *
* R * A * E
R * D * E *

MUSICAL EPITAPHS

27. Over the grave of a French musician, who was choked by a fish bone, the following epitaph was inscribed in notes of music:--A. G. A. E. A.

Over the porch of the house of Gustave Doré these musical notes were placed on a tablet:--C. E. B. A. C. D.

What do these inscriptions signify?

QUITE TOO TOO

28. “Where can we meet to-morrow?” said Jack Spooner to his best girl.

“We will go,” she replied, “at 222222222222 LEY STREET.”

When and where did they meet?

A BROKEN WORD

29. What does this spell?

C
-------------------
T T T T T T T T T T

CONTRADICTORY TERMS

30. What English word is it which may be so treated as to affirm or disallow the use of its own initial or final letter?

PRINTERS’ PIE

31. Can you arrange these letters

E I O O O U
B C N N R R S S

so that they form the title of a book well-known to boys?

FILL IN THE GAPS

32. Keeping these letters in their present order make a sensible sentence by inserting among them as often as is necessary another letter, which must be in every case the same.

A DEN I I CAN DOCK.

DISTORTED SHAKESPEARE

33. Here is a well-known quotation from Shakespeare, which seems to need some straightening out:--

OXXU8 MAAULGIHCTE
NOR

A PHONETIC NIGHTMARE

34. Here, as an awful warning to those who are ready to accept the definition of English spelling given by a former headmaster of Winchester--“Consonants are interchangeable, and vowels do not count”--is a common English word of twelve letters, in “linked sweetness long drawn out.”

Iewkngheaurrhphthewempeighghtips.

Can you decipher it?

ANOTHER WORD SQUARE

35. Can you, by filling in letters, complete this word square so that it shall read alike across and from top to bottom?

* A * *
A * * A
* E * *
* A * E

A QUAINT INSCRIPTION

36. The following curious inscription may be seen on a card hanging up in the bar of an old riverside inn in Norfolk:--

THEM * ILL * ERSLEA * VET * HEMI
LLT * HEW * HER * RYMEN * LOW
ERTH * EIRS * AILTH * EMA
LTS * TER * SLE * AVET * HE * KI
LN * FORAD * ROPO * FTH
EWHI * TESW * AN * SALE.

Can you decipher it?

A POET’S PI

37. TONDEBNIOTOCHUMFOARYHUR
OTDIRECTTHAWHOTERSOFKLSYA;
TIKATESTUBALIGHTSTILLETRUFLYR
OTBOWLALLNEFESLEAVARFWYAA.

In this printer’s pie the words are in their proper sequence, but the letters are tangled.

BURIED PLACES

38. In the following short sentences five names of places are buried--that is to say, the letters which spell them in proper order form parts of more words than one. Thus, for example “Paris” might be buried in the words “go u_p a ris_e:”

“The men could ride all on donkeys, the skipper, though, came to a bad end.”

When you have discovered these places, try to find out what very unexpected word of more than four letters is buried in the sentence, “On Christmas Eve you rang out angel peals.”

TREASON CONDONED

39. According to an old poet, Sir John Harrington (1561-1612):--

“Treason doth never flourish; what’s the reason?
For if it prosper none dare call it treason!”

The classic lines may possibly have been the germ of the flippant modern riddle, “Why is it no offence to conspire in the evening?”

A BIT OF BOTANY

40. Inscribe an _m_ above a line
And write an _e_ below,
This woodland flower is hung so fine
It bends when zephyrs flow.

A PIED PROVERB

41. The following letters, if they are properly rearranged, will fall into the words which form a popular proverb:--

AAEEGGHILLMNNNOOOORRSSSSTT

Can you place them in position?

A DROP LETTER PUZZLE

42. Can you fill in the gaps of this proverb?

E**t* *e*s**s *a*e *h* *o** **i*e.

MULTUM IN PARVO

43. There is an English word of five syllables which has only eight letters, five of them vowels--an a, an e, twice i, and y. What are its consonants?

DOUBLETS

44. Can you turn TORMENT to RAPTURE, using four links, changing only one letter each time, and varying the order of the letters?

A PIED PROVERB

45. Can you arrange these letters so that they form a sentence of five words?

aaceeeffhhiiiiimnnoooprrssttttt.

The result is a well-known English proverb.

WHAT CAN IT BE?

46. Add one letter, and make this into a sensible English sentence:--

GDLDPRTFRRTHDXXFRDDNS

OUT OF PROPORTION

47. One vowel in an English word is found,
Which by eight consonants is hedged around.

48. Can you form an English word with these letters?

AAAAABBNNIIRSSTT.

49. What is this? It is found in Shakespeare:--

K I N I.

ALPHA BETA

50. There are two English words which contain each of them ten letters, and six of these are a, b, c, d, e, f, the first six letters of the alphabet. Can you build up either or both of them without looking at the solution?

SHIFTING NUMBERS

51. Of a band of true kinsmen I stand at the head,
Who, to keep themselves warm, cluster three in a bed.
Put four into gaol and their number has risen,
So that six can be counted together in prison.
Take the six and recount them, they dwindle to three;
Count again, and a change into five you will see.
With no number from one to one hundred I mix,
Yet with five of my mates I am seen to make six.

AN IMPUDENT PRODIGAL

52. The prodigal son of a wealthy colonial farmer received a letter from his father, to suggest that a considerable part of his inheritance should be safeguarded before he squandered it. His reply ran thus:--“Dear dad, keep 1000050.” As such a sum, even in dollars, was out of the question, the father was completely puzzled.

What did the prodigal mean?

BURIED POETS

53. The names of eight famous British poets are buried in these lines, that is to say, the letters that spell the names form in their proper order parts of different words:--

The sun is darting rays of gold
Upon the moor, enchanting spot,
Whose purpled heights, by Ronald loved,
Up open to his Shepherd cot.

And sundry denizens of air
Are flying, aye, each to his nest;
And eager make at such an hour
All haste to reach the mansions-blest.

Can you dig them up?

A FATEFUL LETTER

54. When _A. B._ gave up the reins of government, and _C. B._ took office in his place, it was found that their political positions could be exactly described by two quite common English verbs, which differ only in this, that the one is longer by one letter than the other, while the rest of the letters are the same, and in the same order. What are these two verbs?

A PRIZE REBUS

55. The following is a prize Rebus:--

done |
mutt | a glutt
and |
i | T. c. d.
you make me

A LETTER TANGLE

56. First a _c_ and _a_ _t_, last _a_ _c_ and a _t_,
With a couple of letters between,
Form a sight that our eyes are delighted to see,
Unless in their sight it is seen.

A TRANSPOSITION

57. Cut off my tail and set it at my head,
What was an island is a little bear instead.

A REBUS

T S.

58. What English word do these two letters indicate? There are two possible solutions of equal merit.

A PHONETIC PHRASE

59. How can we read this?

I N X I N X I N.

A GOOD END

60.

SOLUTIONS

CHESS CAMEOS

No. XXVI

Black has made the false move Kt from Q sq to Kt 3. When this is replaced, and the king is moved as the proper penalty, White mates at once with one or other of the Knights.

No. XXVII

Replace the White Kt at B 7, and a Black Pawn at K 4; then P takes P _en pas_. Mate.

ANALYSIS AND PROOF

It can be proved that Black’s last move _must have been_ P from K 2 to K 4, so that White may take the P _en pas_.

The Black King cannot have moved from any _occupied_ square.

(The White Kt now occupies B 7.)

Nor from Kt 3 or 4, as both are now _doubly_ guarded, so that he cannot have moved _out of a check_.

(The White Kt now helps to guard Kt 5.)

Nor can he have moved from K 2, as the White P on Q 6 cannot have moved _to give check_.

No other P can have moved.

The K P cannot have moved from K 3, became of the position of the White King.

Therefore Black’s last move _must have been_ P from K 2 to K 4, which White can take _en pas_ giving Mate.

No. XXVIII

B--Q 2 B--R 5 P--Kt 4
-------- ---------------- ------- White has no move.
P--R 7 P--R 7 becomes Q any

The way in which the B runs to earth and is shut in is most ingenious. Black with the new Q cannot anyhow give White a move.

No. XXIX

R--Kt 7, ch. R--Kt 5 R--B 5, ch.
------------ ----------- -----------------
K moves P becomes Q Q × R, stalemate.

No. XXX

B--Kt 8.

No. XXXI

B--R 4.

No. XXXII

B--R sq.

No. XXXIII

B--Q 4.

No. XXXIV

B--B sq.

No. XXXV

K--R 4.

No. XXXVI

Kt--Kt’s 6.

No. XXXVII

R--Kt 5 Kt--B 6 Kt × Kt mate.
------- ----------- -------------
Kt × R Kt--B 6 ch.

No. XXXVIII

Kt--R 7 Q--KB 8 Q--R 8 mate.
------- --------- ------------
B moves B returns

Any other move of the Kt would impede the movements of the Q.

No. XXXIX

R--R sq. Q--Kt sq. Q to Kt sq. mate.
-------- ---------- -----------------
B moves. B returns.

No. XL

This beautiful problem is solved by:--

Q--Kt 6 K--B 2 mates accordingly.
------- ------ ------------------
P × Q any

or

R--B 3 mates accordingly.
------- ------ ------------------
Kt--K 3 any

No. XLI

R--R 2. Q--R sq. Q mates.
------- -------- --------
B × Kt any

if

Kt--QB 8, Q or Kt mates.
-------- --------- --------------
B--Q sq. any

if

Kt--QB 6, Q or Kt mates.
----------- --------- --------------
B elsewhere any

No. XLII

Kt--Kt 4, dis. ch. Q--KR 2, ch. Kt--B 2, mate.
------------------ ------------ --------------
K--R 8. P × Q.

There are other variations.

No. XLIII

B--Kt sq. Q--QR 7, Q mates.
--------- -------- --------
P × Kt, K × Kt.

If K × Kt, Q × P, and mates next move.

No. XLIV

K--Q 7, R--Q 5, Q mates.
------- ------- --------
K moves K × R

No. XLV

R--Q 8 Q × P, ch. B mates.
------- ---------- --------
K moves K × Q

if

Q--K 7 Q mates.
------- ------ --------
B moves any

No. XLVI

B--B 6 Q--Q 7, ch. R mates.
------ ----------- --------
K × R K × Q

if

R--B 6, ch. Q mates.
----- ----------- --------
B × R K × P

There are other variations.

No. XLVII

Q--R 8 Kt--B 6 mates accordingly.
------ ------- ------------------
Kt × Q any

No. XLVIII

B--Kt 8 Q × B, ch. Q--QR 7, mate.
--------- ---------- --------------
B--K Kt 2 Kt--K 4

if

Q--Q 2, ch. P mates.
------ ----------- --------
B--B 3 K moves

No. XLIX

B-Kt 2 Q--K 3 ch. mates.
------ ---------- ------
K--K 4 any

There are other variations.

No. L

Q--KR 2 Q--Q 6, ch. Kt--K 5. double ch. mate.
------------- ----------- -------------------------
K--B 3 or B 4 Q × Q

There are other variations.

No. LI

R--QR sq. R--R 2 P mates.
--------- ------ --------
P moves P × R

No. LII

Q--B sq. Q × BP ch. Q mates.
-------- ---------- --------
P--K 7 K--Q 3

if

Q × BP ch. Q mates.
------ ---------- --------
K--Q 2 K--B 3

There are other variations.

No. LIII

B--R 8 Q--QR sq. Q--QKt. 7, mate.
------ --------- ----------------
K--R 2 K moves

No. LIV

Q--R 5 Kt--Kt 5 Kt mates.
--------------- -------- ---------
B × Q or B--B 2 any

No. LV

K--Kt 7 Q--Q 5, ch. Kt. mates.
------- ----------- ----------
Kt--B 3 Kt × Q

if

Q--B 8, ch. Q mates.
------- ------- --------
P--K 3 K moves

No. LVI

R--Kt 6 B--Kt 4 R × P mate.
------- ------- -----------
P moves P × B

No. LVII

Kt from R 3--Kt 5 B--B 4 P--Q 4 ch. R--B 5 mate.
----------------- ------ -------------- ------------
P × Kt P × B P × P _en pas_

if

R--Kt 5 ch. mates accordingly.
----- ----------- ------------------
R × B any

and if

Kt--Q 6 R--B 5 ch. Kt--B 7 mate.
------ ------- ---------- -------------
Q--K 6 Q--Kt 3 Q × R

SCIENCE AT PLAY

No. LVIII.--THE GEARED WHEELS

The arrow head at the top of a small wheel with ten teeth, which is geared into and revolved round a large fixed wheel with forty teeth, will point directly upwards five times in its course round the large wheel. Four of these turnings are due to the rotation of the small wheel on its own axis, and one of them results from its revolution round the large wheel.

No. LX.--THE FIFTEEN BRIDGES

It is possible to pass over all the bridges which connect the islands _A_ and _B_ and the banks of the surrounding river without going over any of them twice.

The course can be shown thus, using capital letters for the different regions of land, and italics for the bridges:--E_a_ F_b_ B_c_ F_d_ A_e_ F_f_ C_g_ A_h_ C_i_ D_k_ A_m_ E_n_ A_p_ B_q_ E_l_D.

This order of the bridges can, of course, be reversed.

No. LXVI.--A DUCK HUNT

In order that a spaniel starting from the middle of a circular pond, and going at the same pace as a duck that is swimming round its edge, shall be sure to catch it speedily, the dog must always keep in the straight line between the duck and the centre of the pond.

The duck can never gain an advantage by turning back, and if it swims on continuously in a circle it will be overtaken when it has passed through a quarter of the circumference, for the dog will in the same time have described a semi-circle whose diameter is the radius of the pond, ending at the point where the duck is caught.

No. LXIX.--THE TETHERED BIRD

When a bird tethered by a cord 50 feet long to a post 6 inches in diameter uncoils the full length of the cord, and recoils it in the opposite direction, keeping it always taut, it flies 10,157 feet, or very nearly 2 miles, in its double course.

To avoid possible misunderstanding, we point out that, in order to pass from the uncoiling to the recoiling position, the bird must fly through a semicircle at the end of the fully extended cord.

No. LXX.--THE MOVING DISC AND THE FLY

When a fly, starting from the point _A_, just outside the revolving disc, and always making straight for its mate at the point _B_, crosses the disc in four minutes, during which time the disc is turning twice, the revolution of the disc has a most curious and interesting effect on the path of the fly.

The fly is a quarter of a minute in passing from the outside circle to the next, during which the disc has made an eighth of a revolution, and the fly has reached the point marked 1. The succeeding points up to 16 show the position of the fly at each quarter of a minute, until, by a prettily repeated curve, _B_ is reached.

No. LXXI.--A SHUNTING PUZZLE

The following method enables the engine _R_ to interchange the positions of the wagons, _P_ and _Q_, for either of which there is room on the straight rails at _A_, while there is not room there for the engine, which, if it runs up either siding, must return the same way:--

1. _R_ pushes _P_ into _A_. 2. _R_ returns, pushes _Q_ up to _P_ in _A_, couples _Q_ to _P_, draws them both out to _F_, and then pushes them to _E_. 3. _P_ is now uncoupled, _R_ takes _Q_ back to _A_, and leaves it there. 4. _R_ returns to _P_, pulls _P_ back to _C_, and leaves it there. 5. _R_, running successively through _F_, _D_, _B_, comes to _A_, draws _Q_ out, and leaves it at _B._

No. LXXV.--PHARAOH’S SEAL

It is quite puzzling to decide how many similar triangles or pyramids are expressed on the seal of Pharaoh. There are in fact 96.

No. LXXVI.--ROUND THE GARDEN

The four persons who started at noon from the central fountain, and walked round the four paths at the rates of two, three, four, and five miles an hour would meet for the third time at their starting point at one o’clock, if the distance on each track was one-third of a mile.

No. LXXVII.--A JOINER’S PUZZLE

This diagram shows how to divide Fig. _A_ into two parts, and so rearrange these that they form either Fig. _B_ or Fig. _C_, without turning either of the pieces.

+--------------+
| |
+--------------+ | +--+
| | | |
| +--+ +--------------+--+ | +--+
| | | | | | | | |
| +--+ | | +--+ | | +--+ |
| | | | | | | | |
| +--+ | | +--+ | | +--+ |
| | | | | | | | |
| +--+ | | +--+ | +--+ |
| | | | | | | |
+--+ | | +--+ | +--+ |
| | | | | | |
+--------------+ +--+--------------+ +--------------+
A B C

Cut the five steps, and shift the two pieces as is shown.

No. LXXVIII.--THE BROKEN OCTAGON

The Broken Octagon is repaired and made perfect if its pieces are put together thus:--

No. LXXIX.--AT A DUCK POND

The pond was doubled in size without disturbing the duck-houses, thus:--

+-----------○-----------+
| / \ |
| / \ |
| / \ |
| / \ |
| / \ |
○ ○
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
+-----------○-----------+

No. LXXX.--ALL ON THE SQUARE

This is a perfect arrangement:--

No. LXXXI.--PINS AND DOTS

The pins may be placed thus:--

On the third dot in the top line; on the sixth dot in the second line; on the second dot in the third line; on the fifth dot in the fourth line; on the first dot in the fifth line; on the fourth dot in the sixth line.

*-----------*-----------*-----------*-----------*-----------*
| \ / | \ / | \ / | \ / | \ / |
| \ / | \ / | \ / | \ / | \ / |
| * | * | * | * | * |
| / \ | / \ | / \ | / \ | / \ |
| / \ | / \ | / \ | / \ | / \ |
*-----------*-----------*-----------*-----------*-----------*
| \ / | \ / | \ / | \ / | \ / |
| \ / | \ / | \ / | \ / | \ / |
| * | * | * | * | * |
| / \ | / \ | / \ | / \ | / \ |
| / \ | / \ | / \ | / \ | / \ |
*-----------*-----------*-----------*-----------*-----------*
| \ / | \ / | \ / | \ / | \ / |
| \ / | \ / | \ / | \ / | \ / |
| * | * | * | * | * |
| / \ | / \ | / \ | / \ | / \ |
| / \ | / \ | / \ | / \ | / \ |
*-----------*-----------*-----------*-----------*-----------*
| \ / | \ / | \ / | \ / | \ / |
| \ / | \ / | \ / | \ / | \ / |
| * | * | * | * | * |
| / \ | / \ | / \ | / \ | / \ |
| / \ | / \ | / \ | / \ | / \ |
*-----------*-----------*-----------*-----------*-----------*
| \ / | \ / | \ / | \ / | \ / |
| \ / | \ / | \ / | \ / | \ / |
| * | * | * | * | * |
| / \ | / \ | / \ | / \ | / \ |
| / \ | / \ | / \ | / \ | / \ |
*-----------*-----------*-----------*-----------*-----------*

No. LXXXII.--A TRICKY COURSE

To trace this course draw lines upon the diagram from square 46 to squares 38, 52, 55, 23, 58, 64, 8, 57, 1, 7, 42, 10, 13, 27, and 19. This gives fifteen lines which pass through every square only once.

No. LXXXIII.--FOR THE CHILDREN

Make a square with three on every side, and place the remaining four one on each of the corner men or buttons.

No. LXXXVII.--LOYD’S MITRE PROBLEM

The figure given is thus divided into four equal and similar parts:--

No. LXXXIX.--CUT OFF THE CORNERS

A E F B
+------+--------+------+
| / \ |
| / \ |
|/ \|
M+ +G
| |
| |
| |
L+ +H
|\ /|
| \ / |
| \ / |
+------+--------+------+
C K I D

A very simple rule of thumb method for striking the points in the sides of a square, which will be at the angles of an octagon formed by cutting off equal corners of the square, is to place another square of equal size upon the original one, so that the centre is common to both, and the diagonal of the new square lies upon a diameter of the other parallel to its side.

No. XCIII.--MAKING MANY SQUARES

The subjoined diagram shows how the two oblongs, applied to the two concentric squares, produce 31 perfect squares, namely, 17 small ones, one equal to 25 of these, 5 equal to 9, and 8 equal to 4.

+------+
| |
| |
+-------------+------+-------------+
| | | |
| | | |
| +------+------+------+ |
| | | | | |
| | | | | |
+-----+------+------+------+------+------+------+
| | | | | | | |
| | | | | | | |
+-----+------+------+------+------+------+------+
| | | | | |
| | | | | |
| +------+------+------+ |
| | | |
| | | |
+-------------+------+-------------+
| |
| |
+------+

No. XCIV.--CUT ACROSS