318. LION-HUNTING. My friend Captain Potham Hall, the renowned hunter of big game, says there is nothing more exhilarating than a brush with a herd--a pack--a team--a flock--a swarm (it has taken me a full quarter of an hour to recall the right word, but I have it at last)--a _pride_ of lions. Why a number of lions are called a "pride," a number of whales a "school," and a number of foxes a "skulk" are mysteries of philology into which I will not enter.
97. THE SPOT ON THE TABLE. A boy, recently home from school, wished to give his father an exhibition of his precocity. He pushed a large circular table into the corner of the room, as shown in the illustration, so that it touched both walls, and he then pointed to a spot of ink on the extreme edge.
"Here is a little puzzle for you, pater," said the youth. "That spot is exactly eight inches from one wall and nine inches from the other. Can (1/2)
270. THE GLASS BALLS. A number of clever marksmen were staying at a country house, and the host, to provide a little amusement, suspended strings of glass balls,
as shown in the illustration, to be fired at. After they had all put their skill to a sufficient test, somebody asked the following question:
"What is the total number of different ways in which these sixteen balls may be broken, if we must always break the lowest ball that remains on (1/3)
25. CHINESE MONEY. The Chinese are a curious people, and have strange inverted ways of doing things. It is said that they use a saw with an upward pressure instead of a downward one, that they plane a deal board by pulling the tool toward them instead of pushing it, and that in building a house they first construct the roof and, having raised that into position,
proceed to work downwards. In money the currency of the country consists (1/3)
SOLUTION TO 312. THE FIVE CRESCENTS OF BYZANTIUM. (1/2)
If that ancient architect had arranged his five crescent tiles in the manner shown in the following diagram, every tile would have been watched over by, or in a line with, at least one crescent, and space would have been reserved for a perfectly square carpet equal in area to exactly half of the pavement. It is a very curious fact that, although there are two or three solutions allowing a carpet to be laid down
312. THE FIVE CRESCENTS OF BYZANTIUM. When Philip of Macedon, the father of Alexander the Great, found himself confronted with great difficulties in the siege of Byzantium, he set his men to undermine the walls. His desires, however, miscarried, for no sooner had the operations been begun than a crescent moon suddenly appeared in the heavens and discovered his plans to his adversaries. The Byzantines were naturally elated, and in order to show their gratitude (1/4)
167. THE WIZARD'S CATS. A wizard placed ten cats inside a magic circle as shown in our illustration, and hypnotized them so that they should remain stationary during his pleasure. He then proposed to draw three circles inside the large one, so that no cat could approach another cat without crossing a magic circle. Try to draw the three circles so that every cat has its own enclosure and cannot reach another cat without crossing a line.
SOLUTION TO 403. THE SPANISH DUNGEON. (1/6)
| | | | | | | | | |
| 1 | 2 | 3 | 4 | | 10 | 9 | 7 | 4 |
| | | | | | | | | |
| 5 | 6 | 7 | 8 | | 6 | 5 | 11 | 8 |
403. THE SPANISH DUNGEON. Not fifty miles from Cadiz stood in the middle ages a castle, all traces of which have for centuries disappeared. Among other interesting features, this castle contained a particularly unpleasant dungeon divided into sixteen cells, all communicating with one another, as shown in the illustration.
Now, the governor was a merry wight, and very fond of puzzles withal. One day he went to the dungeon and said to the prisoners, "By my (1/4)
SOLUTION TO 225. THE TEN PRISONERS.
It will be seen in the illustration how the prisoners may be arranged so as to produce as many as sixteen even rows. There are 4 such vertical rows, 4 horizontal rows, 5 diagonal rows in one direction, and 3 diagonal rows in the other direction. The arrows here show the movements of the four prisoners, and it will be seen that the infirm man in the bottom corner has not been moved.
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 (1/3)
352. IMMOVABLE PAWNS. Starting from the ordinary arrangement of the pieces as for a game, what is the smallest possible number of moves necessary in order to arrive at the following position? The moves for both sides must, of course, be played strictly in accordance with the rules of the game, though the result will necessarily be a very weird kind of chess.
SOLUTION TO 153. A CUTTING-OUT PUZZLE. (1/3)
The illustration shows how to cut the four pieces and form with them a square. First find the side of the square (the mean proportional between the length and height of the rectangle), and the method is obvious. If our strip is exactly in the proportions 9 × 1, or 16 × 1, or 25 × 1, we can clearly cut it in 3, 4, or 5 rectangular pieces respectively to form a square. Excluding these special cases, the general law is that for a
153. A CUTTING-OUT PUZZLE. Here is a little cutting-out poser. I take a strip of paper, measuring five inches by one inch, and, by cutting it into five pieces, the parts fit together and form a square, as shown in the illustration. Now, it is quite an interesting puzzle to discover how we can do this in only four pieces.
260. THE HONEYCOMB PUZZLE. Here is a little puzzle with the simplest possible conditions. Place the point of your pencil on a letter in one of the cells of the honeycomb,
and trace out a very familiar proverb by passing always from a cell to one that is contiguous to it. If you take the right route you will have visited every cell once, and only once. The puzzle is much easier than it looks.
SOLUTION TO 315. THE HAT-PEG PUZZLE. (1/2)
The moves will be made quite clear by a reference to the diagrams, which show the position on the board after each of the four moves. The darts indicate the successive removals that have been made. It will be seen that at every stage all the squares are either attacked or occupied, and that after the fourth move no queen attacks any other. In the case of the last move the queen in the top row might also have been moved one
315. THE HAT-PEG PUZZLE. Here is a five-queen puzzle that I gave in a fanciful dress in 1897. As the queens were there represented as hats on sixty-four pegs, I will keep to the title, "The Hat-Peg Puzzle." It will be seen that every square is occupied or attacked. The puzzle is to remove one queen to a different square so that still every square is occupied or attacked,
then move a second queen under a similar condition, then a third queen, (1/2)
307. THE COLOURED COUNTERS. The diagram represents twenty-five coloured counters, Red, Blue, Yellow,
Orange, and Green (indicated by their initials), and there are five of each colour, numbered 1, 2, 3, 4, and 5. The problem is so to place them in a square that neither colour nor number shall be found repeated in any one of the five rows, five columns, and two diagonals. Can you so rearrange them?
SOLUTION TO 425. JACK AND THE BEANSTALK. (1/2)
The serious blunder that the artist made in this drawing was in depicting the tendrils of
the bean climbing spirally as at A above, whereas the French bean, or scarlet runner, the variety clearly selected by the artist in the absence of any authoritative information on the point, always climbs as shown at B. Very few seem to be aware of this curious little fact. Though the bean always insists on a sinistrorsal growth, as B, the hop
Puzzles from Henry Ernest Dudeney's "Amusements in Mathematics"
A Mastodon instance for maths people. The kind of people who make \(\pi z^2 \times a\) jokes.
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