Section 7 of 27 - Table of Contents
211.--THE TWELVE MINCE-PIES.
It will be seen in our illustration how twelve mince-pies may be placed
on the table so as to form six straight rows with four pies in every
row. The puzzle is to remove only four of them to new positions so that
there shall be _seven_ straight rows with four in every row. Which four
would you remove, and where would you replace them?
[Illustration]
212.--THE BURMESE PLANTATION.
[Illustration]
A short time ago I received an interesting communication from the
British chaplain at Meiktila, Upper Burma, in which my correspondent
informed me that he had found some amusement on board ship on his way
out in trying to solve this little poser.
If he has a plantation of forty-nine trees, planted in the form of a
square as shown in the accompanying illustration, he wishes to know how
he may cut down twenty-seven of the trees so that the twenty-two left
standing shall form as many rows as possible with four trees in every
row.
Of course there may not be more than four trees in any row.
213.--TURKS AND RUSSIANS.
This puzzle is on the lines of the Afridi problem published by me in
_Tit-Bits_ some years ago.
On an open level tract of country a party of Russian infantry, no two of
whom were stationed at the same spot, were suddenly surprised by
thirty-two Turks, who opened fire on the Russians from all directions.
Each of the Turks simultaneously fired a bullet, and each bullet passed
immediately over the heads of three Russian soldiers. As each of these
bullets when fired killed a different man, the puzzle is to discover
what is the smallest possible number of soldiers of which the Russian
party could have consisted and what were the casualties on each side.
MOVING COUNTER PROBLEMS.
"I cannot do't without counters."
_Winter's Tale_, iv. 3.
Puzzles of this class, except so far as they occur in connection with
actual games, such as chess, seem to be a comparatively modern
introduction. Mathematicians in recent times, notably Vandermonde and
Reiss, have devoted some attention to them, but they do not appear to
have been considered by the old writers. So far as games with counters
are concerned, perhaps the most ancient and widely known in old times is
"Nine Men's Morris" (known also, as I shall show, under a great many
other names), unless the simpler game, distinctly mentioned in the works
of Ovid (No. 110, "Ovid's Game," in _The Canterbury Puzzles_), from
which "Noughts and Crosses" seems to be derived, is still more ancient.
In France the game is called Marelle, in Poland Siegen Wulf Myll
(She-goat Wolf Mill, or Fight), in Germany and Austria it is called
Muhle (the Mill), in Iceland it goes by the name of Mylla, while the
Bogas (or native bargees) of South America are said to play it, and on
the Amazon it is called Trique, and held to be of Indian origin. In our
own country it has different names in different districts, such as Meg
Merrylegs, Peg Meryll, Nine Peg o'Merryal, Nine-Pin Miracle, Merry Peg,
and Merry Hole. Shakespeare refers to it in "Midsummer Night's Dream"
(Act ii., scene 1):--
"The nine-men's morris is filled up with mud;
And the quaint mazes in the wanton green,
For lack of tread, are undistinguishable."
It was played by the shepherds with stones in holes cut in the turf.
John Clare, the peasant poet of Northamptonshire, in "The Shepherd Boy"
(1835) says:--"Oft we track his haunts .... By nine-peg-morris nicked
upon the green." It is also mentioned by Drayton in his "Polyolbion."
It was found on an old Roman tile discovered during the excavations at
Silchester, and cut upon the steps of the Acropolis at Athens. When
visiting the Christiania Museum a few years ago I was shown the great
Viking ship that was discovered at Gokstad in 1880. On the oak planks
forming the deck of the vessel were found boles and lines marking out
the game, the holes being made to receive pegs. While inspecting the
ancient oak furniture in the Rijks Museum at Amsterdam I became
interested in an old catechumen's settle, and was surprised to find the
game diagram cut in the centre of the seat--quite conveniently for
surreptitious play. It has been discovered cut in the choir stalls of
several of our English cathedrals. In the early eighties it was found
scratched upon a stone built into a wall (probably about the date 1200),
during the restoration of Hargrave church in Northamptonshire. This
stone is now in the Northampton Museum. A similar stone has since been
found at Sempringham, Lincolnshire. It is to be seen on an ancient
tombstone in the Isle of Man, and painted on old Dutch tiles. And in
1901 a stone was dug out of a gravel pit near Oswestry bearing an
undoubted diagram of the game.
The game has been played with different rules at different periods and
places. I give a copy of the board. Sometimes the diagonal lines are
omitted, but this evidently was not intended to affect the play: it
simply meant that the angles alone were thought sufficient to indicate
the points. This is how Strutt, in _Sports and Pastimes_, describes the
game, and it agrees with the way I played it as a boy:--"Two persons,
having each of them nine pieces, or men, lay them down alternately, one
by one, upon the spots; and the business of either party is to prevent
his antagonist from placing three of his pieces so as to form a row of
three, without the intervention of an opponent piece. If a row be
formed, he that made it is at liberty to take up one of his competitor's
pieces from any part he thinks most to his advantage; excepting he has
made a row, which must not be touched if he have another piece upon the
board that is not a component part of that row. When all the pieces are
laid down, they are played backwards and forwards, in any direction that
the lines run, but only can move from one spot to another (next to it)
at one time. He that takes off all his antagonist's pieces is the
conqueror."
[Illustration]
214.--THE SIX FROGS.
[Illustration]
The six educated frogs in the illustration are trained to reverse their
order, so that their numbers shall read 6, 5, 4, 3, 2, 1, with the blank
square in its present position. They can jump to the next square (if
vacant) or leap over one frog to the next square beyond (if vacant),
just as we move in the game of draughts, and can go backwards or
forwards at pleasure. Can you show how they perform their feat in the
fewest possible moves? It is quite easy, so when you have done it add a
seventh frog to the right and try again. Then add more frogs until you
are able to give the shortest solution for any number. For it can always
be done, with that single vacant square, no matter how many frogs there
are.
215.--THE GRASSHOPPER PUZZLE.
It has been suggested that this puzzle was a great favourite among the
young apprentices of the City of London in the sixteenth and seventeenth
centuries. Readers will have noticed the curious brass grasshopper on
the Royal Exchange. This long-lived creature escaped the fires of 1666
and 1838. The grasshopper, after his kind, was the crest of Sir Thomas
Gresham, merchant grocer, who died in 1579, and from this cause it has
been used as a sign by grocers in general. Unfortunately for the legend
as to its origin, the puzzle was only produced by myself so late as the
year 1900. On twelve of the thirteen black discs are placed numbered
counters or grasshoppers. The puzzle is to reverse their order, so that
they shall read, 1, 2, 3, 4, etc., in the opposite direction, with the
vacant disc left in the same position as at present. Move one at a time
in any order, either to the adjoining vacant disc or by jumping over one
grasshopper, like the moves in draughts. The moves or leaps may be made
in either direction that is at any time possible. What are the fewest
possible moves in which it can be done?
[Illustration]
216.--THE EDUCATED FROGS.
[Illustration]
Our six educated frogs have learnt a new and pretty feat. When placed on
glass tumblers, as shown in the illustration, they change sides so that
the three black ones are to the left and the white frogs to the right,
with the unoccupied tumbler at the opposite end--No. 7. They can jump to
the next tumbler (if unoccupied), or over one, or two, frogs to an
unoccupied tumbler. The jumps can be made in either direction, and a
frog may jump over his own or the opposite colour, or both colours. Four
successive specimen jumps will make everything quite plain: 4 to 1, 5 to
4, 3 to 5, 6 to 3. Can you show how they do it in ten jumps?
217.--THE TWICKENHAM PUZZLE.
[Illustration:
( I ) ((N))
( M ) ((A))
( H ) ((T))
( E ) ((W))
( C ) ((K))
( )
]
In the illustration we have eleven discs in a circle. On five of the
discs we place white counters with black letters--as shown--and on five
other discs the black counters with white letters. The bottom disc is
left vacant. Starting thus, it is required to get the counters into
order so that they spell the word "Twickenham" in a clockwise direction,
leaving the vacant disc in the original position. The black counters
move in the direction that a clock-hand revolves, and the white counters
go the opposite way. A counter may jump over one of the opposite colour
if the vacant disc is next beyond. Thus, if your first move is with K,
then C can jump over K. If then K moves towards E, you may next jump W
over C, and so on. The puzzle may be solved in twenty-six moves.
Remember a counter cannot jump over one of its own colour.
218.--THE VICTORIA CROSS PUZZLE.
[Illustration:
+---------------------+
| \... A .../ |
| (I) |.......| (V) |
|\_____|_______|_____/|
|......| |------|
|.. R .| |. I ..|
|......| |......|
| _____|_______|_____ |
|/ |.......| \|
| (O) |.. T ..| (C) |
| /.........\ |
+---------------------+
]
The puzzle-maker is peculiarly a "snapper-up of unconsidered trifles,"
and his productions are often built up with the slenderest materials.
Trivialities that might entirely escape the observation of others, or,
if they were observed, would be regarded as of no possible moment, often
supply the man who is in quest of posers with a pretty theme or an idea
that he thinks possesses some "basal value."
When seated opposite to a lady in a railway carriage at the time of
Queen Victoria's Diamond Jubilee, my attention was attracted to a brooch
that she was wearing. It was in the form of a Maltese or Victoria Cross,
and bore the letters of the word VICTORIA. The number and arrangement of
the letters immediately gave me the suggestion for the puzzle which I
now present.
The diagram, it will be seen, is composed of nine divisions. The puzzle
is to place eight counters, bearing the letters of the word VICTORIA,
exactly in the manner shown, and then slide one letter at a time from
black to white and white to black alternately, until the word reads
round in the same direction, only with the initial letter V on one of
the black arms of the cross. At no time may two letters be in the same
division. It is required to find the shortest method.
Leaping moves are, of course, not permitted. The first move must
obviously be made with A, I, T, or R. Supposing you move T to the
centre, the next counter played will be O or C, since I or R cannot be
moved. There is something a little remarkable in the solution of this
puzzle which I will explain.
219.--THE LETTER BLOCK PUZZLE.
[Illustration:
+-----+-----+-----+\
| | | | |
| G | E | F | |
| | | | |
+-----+-----+-----+\|
| | | | |
| H | C | B | |
| | | | |
+-----+-----+-----+\|
| |\____| | |
| D || | A | |
| || | | |
+-----+-----+-----+ |
\_________________\|
]
Here is a little reminiscence of our old friend the Fifteen Block
Puzzle. Eight wooden blocks are lettered, and are placed in a box, as
shown in the illustration. It will be seen that you can only move one
block at a time to the place vacant for the time being, as no block may
be lifted out of the box. The puzzle is to shift them about until you
get them in the order--
A B C
D E F
G H
This you will find by no means difficult if you are allowed as many
moves as you like. But the puzzle is to do it in the fewest possible
moves. I will not say what this smallest number of moves is, because the
reader may like to discover it for himself. In writing down your moves
you will find it necessary to record no more than the letters in the
order that they are shifted. Thus, your first five moves might be C, H,
G, E, F; and this notation can have no possible ambiguity. In practice
you only need eight counters and a simple diagram on a sheet of paper.
220.--A LODGING-HOUSE DIFFICULTY.
[Illustration]
The Dobsons secured apartments at Slocomb-on-Sea. There were six rooms
on the same floor, all communicating, as shown in the diagram. The rooms
they took were numbers 4, 5, and 6, all facing the sea. But a little
difficulty arose. Mr. Dobson insisted that the piano and the bookcase
should change rooms. This was wily, for the Dobsons were not musical,
but they wanted to prevent any one else playing the instrument. Now, the
rooms were very small and the pieces of furniture indicated were very
big, so that no two of these articles could be got into any room at the
same time. How was the exchange to be made with the least possible
labour? Suppose, for example, you first move the wardrobe into No. 2;
then you can move the bookcase to No. 5 and the piano to No. 6, and so
on. It is a fascinating puzzle, but the landlady had reasons for not
appreciating it. Try to solve her difficulty in the fewest possible
removals with counters on a sheet of paper.
221.--THE EIGHT ENGINES.
The diagram represents the engine-yard of a railway company under
eccentric management. The engines are allowed to be stationary only at
the nine points indicated, one of which is at present vacant. It is
required to move the engines, one at a time, from point to point, in
seventeen moves, so that their numbers shall be in numerical order round
the circle, with the central point left vacant. But one of the engines
has had its fire drawn, and therefore cannot move. How is the thing to
be done? And which engine remains stationary throughout?
[Illustration]
222.--A RAILWAY PUZZLE.
[Illustration]
Make a diagram, on a large sheet of paper, like the illustration, and
have three counters marked A, three marked B, and three marked C. It
will be seen that at the intersection of lines there are nine
stopping-places, and a tenth stopping-place is attached to the outer
circle like the tail of a Q. Place the three counters or engines marked
A, the three marked B, and the three marked C at the places indicated.
The puzzle is to move the engines, one at a time, along the lines, from
stopping-place to stopping-place, until you succeed in getting an A, a
B, and a C on each circle, and also A, B, and C on each straight line.
You are required to do this in as few moves as possible. How many moves
do you need?
223.--A RAILWAY MUDDLE.
The plan represents a portion of the line of the London, Clodville, and
Mudford Railway Company. It is a single line with a loop. There is only
room for eight wagons, or seven wagons and an engine, between B and C on
either the left line or the right line of the loop. It happened that two
goods trains (each consisting of an engine and sixteen wagons) got into
the position shown in the illustration. It looked like a hopeless
deadlock, and each engine-driver wanted the other to go back to the next
station and take off nine wagons. But an ingenious stoker undertook to
pass the trains and send them on their respective journeys with their
engines properly in front. He also contrived to reverse the engines the
fewest times possible. Could you have performed the feat? And how many
times would you require to reverse the engines? A "reversal" means a
change of direction, backward or forward. No rope-shunting,
fly-shunting, or other trick is allowed. All the work must be done
legitimately by the two engines. It is a simple but interesting puzzle
if attempted with counters.
[Illustration]
224.--THE MOTOR-GARAGE PUZZLE.
[Illustration]
The difficulties of the proprietor of a motor garage are converted into
a little pastime of a kind that has a peculiar fascination. All you need
is to make a simple plan or diagram on a sheet of paper or cardboard and
number eight counters, 1 to 8. Then a whole family can enter into an
amusing competition to find the best possible solution of the
difficulty.
The illustration represents the plan of a motor garage, with
accommodation for twelve cars. But the premises are so inconveniently
restricted that the proprietor is often caused considerable perplexity.
Suppose, for example, that the eight cars numbered 1 to 8 are in the
positions shown, how are they to be shifted in the quickest possible way
so that 1, 2, 3, and 4 shall change places with 5, 6, 7, and 8--that is,
with the numbers still running from left to right, as at present, but
the top row exchanged with the bottom row? What are the fewest possible
moves?
One car moves at a time, and any distance counts as one move. To prevent
misunderstanding, the stopping-places are marked in squares, and only
one car can be in a square at the same time.
225.--THE TEN PRISONERS.
If prisons had no other use, they might still be preserved for the
special benefit of puzzle-makers. They appear to be an inexhaustible
mine of perplexing ideas. Here is a little poser that will perhaps
interest the reader for a short period. We have in the illustration a
prison of sixteen cells. The locations of the ten prisoners will be
seen. The jailer has queer superstitions about odd and even numbers, and
he wants to rearrange the ten prisoners so that there shall be as many
even rows of men, vertically, horizontally, and diagonally, as
possible. At present it will be seen, as indicated by the arrows, that
there are only twelve such rows of 2 and 4. I will state at once that
the greatest number of such rows that is possible is sixteen. But the
jailer only allows four men to be removed to other cells, and informs me
that, as the man who is seated in the bottom right-hand corner is
infirm, he must not be moved. Now, how are we to get those sixteen rows
of even numbers under such conditions?
[Illustration]
226.--ROUND THE COAST.
[Illustration]
Here is a puzzle that will, I think, be found as amusing as instructive.
We are given a ring of eight circles. Leaving circle 8 blank, we are
required to write in the name of a seven-lettered port in the United
Kingdom in this manner. Touch a blank circle with your pencil, then jump
over two circles in either direction round the ring, and write down the
first letter. Then touch another vacant circle, jump over two circles,
and write down your second letter. Proceed similarly with the other
letters in their proper order until you have completed the word. Thus,
suppose we select "Glasgow," and proceed as follows: 6--1, 7--2, 8--3,
7--4, 8--5, which means that we touch 6, jump over 7 and and write down
"G" on 1; then touch 7, jump over 8 and 1, and write down "l" on 2; and
so on. It will be found that after we have written down the first five
letters--"Glasg"--as above, we cannot go any further. Either there is
something wrong with "Glasgow," or we have not managed our jumps
properly. Can you get to the bottom of the mystery?
227.--CENTRAL SOLITAIRE.
[Illustration]
This ancient puzzle was a great favourite with our grandmothers, and
most of us, I imagine, have on occasions come across a "Solitaire"
board--a round polished board with holes cut in it in a geometrical
pattern, and a glass marble in every hole. Sometimes I have noticed one
on a side table in a suburban front parlour, or found one on a shelf in
a country cottage, or had one brought under my notice at a wayside inn.
Sometimes they are of the form shown above, but it is equally common for
the board to have four more holes, at the points indicated by dots. I
select the simpler form.
Though "Solitaire" boards are still sold at the toy shops, it will be
sufficient if the reader will make an enlarged copy of the above on a
sheet of cardboard or paper, number the "holes," and provide himself
with 33 counters, buttons, or beans. Now place a counter in every hole
except the central one, No. 17, and the puzzle is to take off all the
counters in a series of jumps, except the last counter, which must be
left in that central hole. You are allowed to jump one counter over the
next one to a vacant hole beyond, just as in the game of draughts, and
the counter jumped over is immediately taken off the board. Only
remember every move must be a jump; consequently you will take off a
counter at each move, and thirty-one single jumps will of course remove
all the thirty-one counters. But compound moves are allowed (as in
draughts, again), for so long as one counter continues to jump, the
jumps all count as one move.
Here is the beginning of an imaginary solution which will serve to make
the manner of moving perfectly plain, and show how the solver should
write out his attempts: 5-17, 12-10, 26-12, 24-26 (13-11, 11-25), 9-11
(26-24, 24-10, 10-12), etc., etc. The jumps contained within brackets
count as one move, because they are made with the same counter. Find the
fewest possible moves. Of course, no diagonal jumps are permitted; you
can only jump in the direction of the lines.
228.--THE TEN APPLES.
[Illustration]
The family represented in the illustration are amusing themselves with
this little puzzle, which is not very difficult but quite interesting.
They have, it will be seen, placed sixteen plates on the table in the
form of a square, and put an apple in each of ten plates. They want to
find a way of removing all the apples except one by jumping over one at
a time to the next vacant square, as in draughts; or, better, as in
solitaire, for you are not allowed to make any diagonal moves--only
moves parallel to the sides of the square. It is obvious that as the
apples stand no move can be made, but you are permitted to transfer any
single apple you like to a vacant plate before starting. Then the moves
must be all leaps, taking off the apples leaped over.
229.--THE NINE ALMONDS.
"Here is a little puzzle," said a Parson, "that I have found peculiarly
fascinating. It is so simple, and yet it keeps you interested
indefinitely."
The reverend gentleman took a sheet of paper and divided it off into
twenty-five squares, like a square portion of a chessboard. Then he
placed nine almonds on the central squares, as shown in the
illustration, where we have represented numbered counters for
convenience in giving the solution.
"Now, the puzzle is," continued the Parson, "to remove eight of the
almonds and leave the ninth in the central square. You make the removals
by jumping one almond over another to the vacant square beyond and
taking off the one jumped over--just as in draughts, only here you can
jump in any direction, and not diagonally only. The point is to do the
thing in the fewest possible moves."
The following specimen attempt will make everything clear. Jump 4 over
1, 5 over 9, 3 over 6, 5 over 3, 7 over 5 and 2, 4 over 7, 8 over 4. But
8 is not left in the central square, as it should be. Remember to remove
those you jump over. Any number of jumps in succession with the same
almond count as one move.
[Illustration]
230.--THE TWELVE PENNIES.
Here is a pretty little puzzle that only requires twelve pennies or
counters. Arrange them in a circle, as shown in the illustration. Now
take up one penny at a time and, passing it over two pennies, place it
on the third penny. Then take up another single penny and do the same
thing, and so on, until, in six such moves, you have the coins in six
pairs in the positions 1, 2, 3, 4, 5, 6. You can move in either
direction round the circle at every play, and it does not matter
whether the two jumped over are separate or a pair. This is quite easy
if you use just a little thought.
[Illustration]
231.--PLATES AND COINS.
Place twelve plates, as shown, on a round table, with a penny or orange
in every plate. Start from any plate you like and, always going in one
direction round the table, take up one penny, pass it over two other
pennies, and place it in the next plate. Go on again; take up another
penny and, having passed it over two pennies, place it in a plate; and
so continue your journey. Six coins only are to be removed, and when
these have been placed there should be two coins in each of six plates
and six plates empty. An important point of the puzzle is to go round
the table as few times as possible. It does not matter whether the two
coins passed over are in one or two plates, nor how many empty plates
you pass a coin over. But you must always go in one direction round the
table and end at the point from which you set out. Your hand, that is to
say, goes steadily forward in one direction, without ever moving
backwards.
[Illustration]
232.--CATCHING THE MICE.
[Illustration]
"Play fair!" said the mice. "You know the rules of the game."
"Yes, I know the rules," said the cat. "I've got to go round and round
the circle, in the direction that you are looking, and eat every
thirteenth mouse, but I must keep the white mouse for a tit-bit at the
finish. Thirteen is an unlucky number, but I will do my best to oblige
you."
"Hurry up, then!" shouted the mice.
"Give a fellow time to think," said the cat. "I don't know which of you
to start at. I must figure it out."
While the cat was working out the puzzle he fell asleep, and, the spell
being thus broken, the mice returned home in safety. At which mouse
should the cat have started the count in order that the white mouse
should be the last eaten?
When the reader has solved that little puzzle, here is a second one for
him. What is the smallest number that the cat can count round and round
the circle, if he must start at the white mouse (calling that "one" in
the count) and still eat the white mouse last of all?
And as a third puzzle try to discover what is the smallest number that
the cat can count round and round if she must start at the white mouse
(calling that "one") and make the white mouse the third eaten.
233.--THE ECCENTRIC CHEESEMONGER.
[Illustration]
The cheesemonger depicted in the illustration is an inveterate puzzle
lover. One of his favourite puzzles is the piling of cheeses in his
warehouse, an amusement that he finds good exercise for the body as well
as for the mind. He places sixteen cheeses on the floor in a straight
row and then makes them into four piles, with four cheeses in every
pile, by always passing a cheese over four others. If you use sixteen
counters and number them in order from 1 to 16, then you may place 1 on
6, 11 on 1, 7 on 4, and so on, until there are four in every pile. It
will be seen that it does not matter whether the four passed over are
standing alone or piled; they count just the same, and you can always
carry a cheese in either direction. There are a great many different
ways of doing it in twelve moves, so it makes a good game of "patience"
to try to solve it so that the four piles shall be left in different
stipulated places. For example, try to leave the piles at the extreme
ends of the row, on Nos. 1, 2, 15 and 16; this is quite easy. Then try
to leave three piles together, on Nos. 13, 14, and 15. Then again play
so that they shall be left on Nos. 3, 5, 12, and 14.
234.--THE EXCHANGE PUZZLE.
Here is a rather entertaining little puzzle with moving counters. You
only need twelve counters--six of one colour, marked A, C, E, G, I, and
K, and the other six marked B, D, F, H, J, and L. You first place them
on the diagram, as shown in the illustration, and the puzzle is to get
them into regular alphabetical order, as follows:--
A B C D
E F G H
I J K L
The moves are made by exchanges of opposite colours standing on the same
line. Thus, G and J may exchange places, or F and A, but you cannot
exchange G and C, or F and D, because in one case they are both white
and in the other case both black. Can you bring about the required
arrangement in seventeen exchanges?
[Illustration]
It cannot be done in fewer moves. The puzzle is really much easier than
it looks, if properly attacked.
235.--TORPEDO PRACTICE.
[Illustration]
If a fleet of sixteen men-of-war were lying at anchor and surrounded by
the enemy, how many ships might be sunk if every torpedo, projected in a
straight line, passed under three vessels and sank the fourth? In the
diagram we have arranged the fleet in square formation, where it will be
seen that as many as seven ships may be sunk (those in the top row and
first column) by firing the torpedoes indicated by arrows. Anchoring the
fleet as we like, to what extent can we increase this number? Remember
that each successive ship is sunk before another torpedo is launched,
and that every torpedo proceeds in a different direction; otherwise, by
placing the ships in a straight line, we might sink as many as thirteen!
It is an interesting little study in naval warfare, and eminently
practical--provided the enemy will allow you to arrange his fleet for
your convenience and promise to lie still and do nothing!
236.--THE HAT PUZZLE.
Ten hats were hung on pegs as shown in the illustration--five silk hats
and five felt "bowlers," alternately silk and felt. The two pegs at the
end of the row were empty.
[Illustration]
The puzzle is to remove two contiguous hats to the vacant pegs, then two
other adjoining hats to the pegs now unoccupied, and so on until five
pairs have been moved and the hats again hang in an unbroken row, but
with all the silk ones together and all the felt hats together.
Remember, the two hats removed must always be contiguous ones, and you
must take one in each hand and place them on their new pegs without
reversing their relative position. You are not allowed to cross your
hands, nor to hang up one at a time.
Can you solve this old puzzle, which I give as introductory to the next?
Try it with counters of two colours or with coins, and remember that the
two empty pegs must be left at one end of the row.
237.--BOYS AND GIRLS.
If you mark off ten divisions on a sheet of paper to represent the
chairs, and use eight numbered counters for the children, you will have
a fascinating pastime. Let the odd numbers represent boys and even
numbers girls, or you can use counters of two colours, or coins.
The puzzle is to remove two children who are occupying adjoining chairs
and place them in two empty chairs, _making them first change sides_;
then remove a second pair of children from adjoining chairs and place
them in the two now vacant, making them change sides; and so on, until
all the boys are together and all the girls together, with the two
vacant chairs at one end as at present. To solve the puzzle you must do
this in five moves. The two children must always be taken from chairs
that are next to one another; and remember the important point of making
the two children change sides, as this latter is the distinctive feature
of the puzzle. By "change sides" I simply mean that if, for example, you
first move 1 and 2 to the vacant chairs, then the first (the outside)
chair will be occupied by 2 and the second one by 1.
[Illustration]
238.--ARRANGING THE JAMPOTS.
I happened to see a little girl sorting out some jam in a cupboard for
her mother. She was putting each different kind of preserve apart on the
shelves. I noticed that she took a pot of damson in one hand and a pot
of gooseberry in the other and made them change places; then she changed
a strawberry with a raspberry, and so on. It was interesting to observe
what a lot of unnecessary trouble she gave herself by making more
interchanges than there was any need for, and I thought it would work
into a good puzzle.
It will be seen in the illustration that little Dorothy has to
manipulate twenty-four large jampots in as many pigeon-holes. She wants
to get them in correct numerical order--that is, 1, 2, 3, 4, 5, 6 on the
top shelf, 7, 8, 9, 10, 11, 12 on the next shelf, and so on. Now, if she
always takes one pot in the right hand and another in the left and makes
them change places, how many of these interchanges will be necessary to
get all the jampots in proper order? She would naturally first change
the 1 and the 3, then the 2 and the 3, when she would have the first
three pots in their places. How would you advise her to go on then?
Place some numbered counters on a sheet of paper divided into squares
for the pigeon-holes, and you will find it an amusing puzzle.
[Illustration]
UNICURSAL AND ROUTE PROBLEMS.
"I see them on their winding way."
REGINALD HEBER.
It is reasonable to suppose that from the earliest ages one man has
asked another such questions as these: "Which is the nearest way home?"
"Which is the easiest or pleasantest way?" "How can we find a way that
will enable us to dodge the mastodon and the plesiosaurus?" "How can we
get there without ever crossing the track of the enemy?" All these are
elementary route problems, and they can be turned into good puzzles by
the introduction of some conditions that complicate matters. A variety
of such complications will be found in the following examples. I have
also included some enumerations of more or less difficulty. These afford
excellent practice for the reasoning faculties, and enable one to
generalize in the case of symmetrical forms in a manner that is most
instructive.
239.--A JUVENILE PUZZLE.
For years I have been perpetually consulted by my juvenile friends about
this little puzzle. Most children seem to know it, and yet, curiously
enough, they are invariably unacquainted with the answer. The question
they always ask is, "Do, please, tell me whether it is really possible."
I believe Houdin the conjurer used to be very fond of giving it to his
child friends, but I cannot say whether he invented the little puzzle or
not. No doubt a large number of my readers will be glad to have the
mystery of the solution cleared up, so I make no apology for introducing
this old "teaser."
The puzzle is to draw with three strokes of the pencil the diagram that
the little girl is exhibiting in the illustration. Of course, you must
not remove your pencil from the paper during a stroke or go over the
same line a second time. You will find that you can get in a good deal
of the figure with one continuous stroke, but it will always appear as
if four strokes are necessary.
[Illustration]
Another form of the puzzle is to draw the diagram on a slate and then
rub it out in three rubs.
240.--THE UNION JACK.
[Illustration]
The illustration is a rough sketch somewhat resembling the British flag,
the Union Jack. It is not possible to draw the whole of it without
lifting the pencil from the paper or going over the same line twice. The
puzzle is to find out just _how much_ of the drawing it is possible to
make without lifting your pencil or going twice over the same line. Take
your pencil and see what is the best you can do.
241.--THE DISSECTED CIRCLE.
How many continuous strokes, without lifting your pencil from the paper,
do you require to draw the design shown in our illustration? Directly
you change the direction of your pencil it begins a new stroke. You may
go over the same line more than once if you like. It requires just a
little care, or you may find yourself beaten by one stroke.
[Illustration]
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