Divided star
which can be reunited to form a perfect cross.
Return todescription
This is a simple way by which the figure given can be divided by four straight cuts into four equal and similarparts—
Divided figure
Return todescription
This is the way to draw twenty-two straight lines within the circle at right-angles to each other, so that they divide it into four similarparts—
Divided circle
and each part has three dots within its borders.
Return todescription
These diagrams show how the upper triangle is divided into five parts, which can be rearranged to form the equilateral triangle below.
Triangle
The originator of this ingenious novelty says, “The method of construction is not shown, but its application is general, and the result is easily verified by measurement.”
Return todescription
This is an arrangement of the twenty-seven counters in nine rows, six in a row, within the borders of an equilateral triangle.
Triangle
Return todescription
All the cards of one colour, when placed alternately, can be brought together in four moves, two at a time,thus—
Image
Place two and three beyond eight;Place five and six between one and four;Place eight and two between four and seven;Place one and five between seven and three.
Return todescription
You can in a moment tell the number chosen on these cards, when you are told on which of them it appears,
I.II.III.IV.13365972346698436681008407210433567993356799537691019417310553769101638701026387010210427410673971103739711037397110311437510794173105104274106124476108124476108114375107114375107134577109134577109134577109144678110144678110144678110154779111154779111154779111154779111174981113185082114205284116245688120195183115195183115215385117255789121215385117225486118225486118265890122235587119235587119235587119275991123255789121265890122286092124286092124275991123275991123296193125296193125296193125306294126306294126306294126316395127316395127316395127316395127V.VI.VII.164880112324896112648096112174981113334997113658197113185082114345098114668298114195183115355199115678399115205284116365210011668841001162153851173753101117698510111722548611838541021187086102118235587119395510311971871031192456881204056104120728810412025578912141571051217389105121265890122425810612274901061222759911234359107123759110712328609212444601081247692108124296193125456110912577931091253062941264662110126789411012631639512747631111277995111127
Image
by adding together the numbers at the top left-hand corner of these.
Return todescription
This diagram shows that the postman can take a course which involves fewer turnings than that indicated, when he had to pass round eighteen corners.
Mail round
It will be seen that he has to turn only fifteen times.
Return todescription
This shows how a square can be divided into three parts, so that these can be reunited to form No. 2 and No. 3 of the diagram.
Square
Three shapes
Try it with scissors and paper or cardboard.
Return todescription
Image
This position fulfils the conditions of the puzzle. Obviously it could not occur in actual play.
Return todescription
The dotted lines in this diagram show where the flag with a cross taken out from its centre must be cut, so that the two pieces can be rejoined to form a perfect flag.
Flag
The piece on the right is moved upward, and to the left.
Return todescription
This is a way in which the eleven parts can be readjusted to form asquare:—
Square
Return todescription
This shows the shortestcourse—
Hospital round
This track takes him completely round every block, passing only once round four of them.
Return todescription
Here is a very simple and symmetrical arrangement, by which on a board of 36 squares twelve counters are so placed that there are two, and two only, on each line, column, and diagonal.
Image
There are other arrangements which fulfil the conditions.
Return todescription
In this nest of triangles of five tiers there are 1196 separate triangles, or nearly double the number (653) of a similar nest of four tiers.
Triangles
In such a figure with 10,000 tiers there would be 6,992,965,420,332 different triangles!
Return todescription
The match puzzle, in which eight matches set in a row are to be rearranged in four pairs, by passing one match over two fourtimes—
Matches
is solved, if the matches are numbered 1, 2, 3, 4, 5, 6, 7, 8, by moving 4 to 7, 6 to 2, 1 to 3, and 5 to 8.
Return todescription
The lower diagram shows how, when three matches are removed from the four squares, theremaining nine can be readjusted to represent threesquares—
Matches
Matches
Return todescription
This diagram shows how different arrangements of four matches are possible in all the thirty-six cells of the square.
Matches
In every case a whole number or a fraction is represented, with such signs or lines as are necessary, and only four matches are used.
Return todescription
It will be seen from the diagram below that the sentence, when filled in as required, is “Rise to vote, sir.”
Image
As this sentence is a perfect palindrome, and reads alike from either end, it can be traced in a great number of different directions.
Return todescription
This subtraction sum may be very neatly worked, without reducing the distances to inches,thus:—
Image
Instead of borrowing one foot, we borrow half-a-foot—i.e., 6 inches; taking 5 from the 6 we have 1 as a remainder; now carrying the 6 inches to the 1 foot, and borrowing half a yard, and subtracting, we have 0 as remainder; carrying the half-yard to the 5 yards, we borrow the full 51⁄2yards, which are one rod, and proceed in the usual manner afterwards, with the result that is shown.
Return todescription
This is an arrangement of nine counters on the irregular board of 67 squares.
Image
No two counters are in the same row, column, or diagonal.
Return todescription
This is the arrangement of nine cards in ten rows, three in eachrow—
Image
Return todescription
The following diagram shows how the two ladies and their squires represented by white Knights and black, and dressed to impersonate Light,Liberty, Love, and Learning, started from the four comer squares, and stepped a figure which exhibited at each pause a revolving square, and in three paces came together in the centre, by a course traced upon the lines of their combined monograms.
Chess moves
Return todescription
The 5 maxims in these 36cells—
Image
are disentangled by reading the lowest line with each of the upper ones in turn. Thus the first maxim runs:—“Never tell all you know, he who tells all he knows often tells what he should not,” and so on throughout.
Return todescription
The dislocated circle is solved by making a single cut through the dotted line shown in the diagram below, and join up the pieces.