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possible pieces that will fit together and form a perfect square. (4/4)

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your compasses at A and with the distance A D describe the arc cutting H B at E. Then place the point of your compasses at D and with the distance D E describe the arc cutting the circumference at F. Now, D F is one of the sides of your pentagon, and you have simply to mark off the other sides round the circle. Quite simple when you know how, but otherwise somewhat of a poser.

Having formed your pentagon, the puzzle is to cut it into the fewest (3/4)

...
round the circumference. But a pentagon is quite another matter. So, as my puzzle has to do with the cutting up of a regular pentagon, it will perhaps be well if I first show my less experienced readers how this figure is to be correctly drawn. Describe a circle and draw the two lines H B and D G, in the diagram, through the centre at right angles. Now find the point A, midway between C and B. Next place the point of (2/4)

155. THE PENTAGON AND SQUARE. I wonder how many of my readers, amongst those who have not given any close attention to the elements of geometry, could draw a regular pentagon, or five-sided figure, if they suddenly required to do so. A regular hexagon, or six-sided figure, is easy enough, for everybody knows that all you have to do is to describe a circle and then, taking the radius as the length of one of the sides, mark off the six points (1/4)

SOLUTION TO 347. COUNTING THE RECTANGLES. (2/2)

SOLUTION TO 347. COUNTING THE RECTANGLES. (1/2)

347. COUNTING THE RECTANGLES. Can you say correctly just how many squares and other rectangles the chessboard contains? In other words, in how great a number of different ways is it possible to indicate a square or other rectangle enclosed by lines that separate the squares of the board?

SOLUTION TO 156. THE DISSECTED TRIANGLE. (2/2)

SOLUTION TO 156. THE DISSECTED TRIANGLE. (1/2)

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Remember that when you have made your five pieces, you must be able, as desired, to put them together to form either the single original triangle or to form two triangles or to form three triangles--all equilateral. (2/2)

156. THE DISSECTED TRIANGLE. A good puzzle is that which the gentleman in the illustration is showing to his friends. He has simply cut out of paper an equilateral triangle--that is, a triangle with all its three sides of the same length. He proposes that it shall be cut into five pieces in such a way that they will fit together and form either two or three smaller equilateral triangles, using all the material in each case. Can you discover how the cuts should be made?
(1/2)

SOLUTION TO 321. THE ROOK'S JOURNEY.

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of the board once and only once, stopping at the square marked 10 at the end of its tenth move, and ending at the square marked 21. Two consecutive moves cannot be made in the same direction--that is to say,
you must make a turn after every move. (2/2)

321. THE ROOK'S JOURNEY. This puzzle I call "The Rook's Journey," because the word "tour"
(derived from a turner's wheel) implies that we return to the point from which we set out, and we do not do this in the present case. We should not be satisfied with a personally conducted holiday tour that ended by leaving us, say, in the middle of the Sahara. The rook here makes twenty-one moves, in the course of which journey it visits every square (1/2)

SOLUTION TO 403. THE SPANISH DUNGEON. (6/6)

SOLUTION TO 403. THE SPANISH DUNGEON. (5/6)

SOLUTION TO 403. THE SPANISH DUNGEON. (4/6)

SOLUTION TO 403. THE SPANISH DUNGEON. (3/6)

SOLUTION TO 403. THE SPANISH DUNGEON. (2/6)

SOLUTION TO 403. THE SPANISH DUNGEON. (1/6)

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