This is a course by which the queen on a chessboard, starting from K R sq., passes over every square in fourteen moves.
“Did you score a score?” said Funniman to his schoolboy nephew, after a local cricket match. “No, uncle,” said the youngster, “but if I had made as many more runs, half as many more, and two runs and a half, I should have made my twenty.” How many runs did he get?
In the “Twentieth Century Standard Puzzle Book” we gave a figure similar to this, in which there were 653 interlacing triangles in four tiers of this character.
We now add a fifth tier at the base, and ask our solvers to determine how many triangles of all shapes and sizes can be counted within its enlarged borders.
Place eight matches in a row, about an inch apart, as indicated in the diagram.
The puzzle is to form these into four pairs in four moves, by moving one match clear over two matches every time.
Place twelve matches, as is shown in the diagram, so that they form four squares.
Now remove three of the matches, and readjust the nine that remain so that they represent three squares.
Edwin and Angelina were far apart, when this message, with its touch of jealous resentment, reached her on the wings of a Marconigram—
“No fickle girl is bonnie to my mind!”
Quite equal to the occasion, she flashed back the reply—
“In love inconstant I no pleasure find!”
How did these messages reveal the places from which they were despatched?
In the four corner and four central cells of this nest of squares four matches are so placed as to represent 1⁄2, 1, 4, 1⁄50, 11, 12, 41, and 49.
Can you, still using only four matches in each case, fit different whole numbers or fractions in similar fashion into the other 28 cells?
Can you complete the top and bottom rows, the two side columns, and the two diagonals of this square by forming in each of them the same sentence so that it can be read in twenty different directions?
| R | I | V | I | R | ||||||||
| I | I | I | I | |||||||||
| V | V | V | ||||||||||
| I | I | I | I | |||||||||
| R | I | V | I | R |
There are four words in the sentence of thirteen letters.
Ask anyone to fix upon a number between 1 and 60 inclusive, and to point out to you the square or squares in which it appears:—
| 3 | 5 | 7 | 9 | 11 | 1 | 5 | 6 | 7 | 13 | 12 | 4 | |
| 13 | 15 | 17 | 19 | 21 | 23 | 14 | 15 | 20 | 21 | 22 | 23 | |
| 25 | 27 | 29 | 31 | 33 | 35 | 28 | 29 | 30 | 31 | 36 | 37 | |
| 37 | 39 | 41 | 43 | 45 | 47 | 52 | 38 | 39 | 44 | 45 | 46 | |
| 49 | 51 | 53 | 55 | 57 | 59 | 47 | 53 | 54 | 55 | 60 | 13 |
| 9 | 10 | 11 | 12 | 13 | 8 | 3 | 6 | 7 | 10 | 11 | 2 | |
| 14 | 15 | 24 | 25 | 26 | 27 | 14 | 15 | 18 | 19 | 22 | 23 | |
| 28 | 29 | 30 | 31 | 40 | 41 | 26 | 27 | 30 | 31 | 34 | 35 | |
| 42 | 43 | 44 | 45 | 46 | 47 | 38 | 39 | 42 | 43 | 46 | 47 | |
| 56 | 57 | 58 | 59 | 60 | 13 | 50 | 51 | 54 | 55 | 58 | 59 |
| 17 | 18 | 19 | 20 | 21 | 16 | 33 | 34 | 35 | 36 | 37 | 32 | |
| 22 | 23 | 24 | 25 | 26 | 27 | 38 | 39 | 40 | 41 | 42 | 43 | |
| 28 | 29 | 30 | 31 | 48 | 49 | 44 | 45 | 46 | 47 | 48 | 49 | |
| 50 | 51 | 52 | 53 | 54 | 55 | 50 | 51 | 52 | 53 | 54 | 55 | |
| 56 | 57 | 58 | 59 | 30 | 60 | 56 | 57 | 58 | 59 | 60 | 41 |
You can find the number at a glance, by simply adding together the numbers in the right-hand top corner cells of the square indicated. Thus, if 45 has been chosen, 32 + 8 + 4 + 1 = 45.
Here is a little subtraction sum, which is not quite so simple as it appears to be:—
| miles | furlongs | rods | yards | feet | inches | |||||||
| 1 | „ | 0 | „ | 0 | „ | 0 | „ | 0 | „ | 0 | ||
| 7 | „ | 39 | „ | 5 | „ | 1 | „ | 5 | ||||
Try it as it stands, without reducing the distance to inches.
Can you, by supplying the missing words, turn a grilse into a salmon? One letter is changed each time, and, except in one case, the order of the letters varies:—
These are the arrangements of the nine digits, by which they add up alike in rows, columns, and diagonals in a square; on all sides in a triangle; and from top to bottom and from side to side in a cross:—
|
|
|
The totals are 15, 20, and 27 respectively.
HAATTCEUMSSSS
The question was asked in a puzzle competition—“Why is every angler ipso facto an Ananias?” Although no such method was asked for or expected, we find that the very letters of the question can be recast into a most apposite reply. Our answer by anagram runs thus—
A liar, .. ..... gay fancies to a ..... ....
Can you complete the sentence by filling in the missing words?
On a board of sixty-seven squares, arranged as is shown in the diagram, place nine counters, so that no two are in the same row, column, or diagonal.
The indentations do not affect the simple conditions.
Can you arrange these nine cards so that they form ten rows with three cards in each row?
| A ♣ |
||||||
| A ♢ |
10 ♡ |
A ♠ |
||||
| Q ♠ |
K ♣ |
K ♢ |
J ♢ |
|||
| K ♡ |
||||||
This may, of course, be done with any nine cards.
Separate these strings of letters into words that scan and rhyme, adding the same missing letter in 55 places.
Two ladies and their squires, here represented by the White Knights and the Black, were dressed to impersonate Light, Liberty, Love, and Learning, and took their places on the corners of a pavement chequered to represent a chessboard, as is shown below:—
| ♘ | ♞ | ||||||
| ♞ | ♘ |
They undertook to step a figure which should exhibit at each pause a revolving square, and in three paces bring them together in the centre, by a course traced upon the lines of their combined monograms. What were their successive steps?
Can you disentangle all this good advice?
| tell | you know | tells | knows | tells | he should not |
| do | you think of | does | thinks of | does | is not good |
| believe | you hear | believes | hears | believes | is false |
| spend | you have | spends | has | spends | he needs |
| judge | you see | judges | sees | judges | is not there |
| never | all | he who | all he | often | what |
It forms 5 excellent maxims in its 36 cells.
Study this quaint figure carefully, and try to discover how it can be divided into two pieces, so that these can be reunited to form a perfect circle.
When Tommy was offered all the money by his uncle if he could place 15 half-crowns and 15 pennies in such order in a circle that, counting always by nines, and starting at a fixed point, he came always upon a penny, and removed it from the circle, he found the key to success in this Latin line, given to him by a school friend, who shared the spoil—“Populeam virgam mater regina ferebat.” The vowels, from a to u, are numbered from 1 to 5, and when they are thus marked in the sentence—
| “ | P | o | p | u | l | e | a | m | v | i | r | g | a | m | m | a | t | e | r | r | e | g | i | n | a | f | e | r | e | b | a | t | , | ” | ||||
| 4 | 5 | 2 | 1 | 3 | 1 | 1 | 2 | 2 | 3 | 1 | 2 | 2 | 1 | |||||||||||||||||||||||||
they show the necessary sequence of half-crowns and pennies.
Start counting with the half-crown marked a, and remove each penny as you come to it on counting up to nine, and the conditions are fulfilled.
This smart advertisement of a polish known as “Old Dutch Cleanser” appeared in an American paper:—
Cleans Scrubs
Scours Polishes
Old Dutch
Cleanser
If the eyes of the proprietor should fall upon this column, he will be surprised to find that his catch words Cleans, Scrubs, Scours, Polishes, can be recast into a perfect anagram, singularly appropriate to the powder advertised.
The opening words of the anagram are “O rub on, sir.”—Can our solvers complete the sentence?
Replace all these 51 pieces on the chessboard, so that no Queen attacks another Queen, no Rook another Rook, no Bishop another Bishop, and no Knight another Knight.
| Q | Q | Q | Q | Q | Q | Q | Q |
| B | B | B | B | B | B | ||
| B | B | ||||||
| B | B | B | B | B | B | ||
| R | R | R | R | R | R | R | R |
| Kt | Kt | Kt | Kt | Kt | |||
| Kt | Kt | Kt | Kt | Kt | Kt | Kt | Kt |
| Kt | Kt | Kt | Kt | Kt | Kt | Kt | Kt |
No account is to be taken of the intervening pieces, but each type of piece is to be considered as if it stood alone upon the board.
Here is a beautifully symmetrical specimen of the Knight’s tour:—