Henry Ernest Dudeney/Modern Puzzles/Geometrical Problems/Dissection Puzzles
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Henry Ernest Dudeney: Modern Puzzles: Geometrical Problems: Dissection Puzzles
$103$ - A New Cutting-out Puzzle
- Cut the figure into four pieces that will fit together and form a square.
$104$ - The Square Table-Top
- A man had three pieces of beautiful wood, measuring $12$ units, $15$ units and $16$ units square respectively.
- He wanted to cut those into the fewest pieces possible that would fit together and form a small square table-tip $25$ units by $25$ units.
- How was he to do it?
$105$ - The Squares of Veneer
- A man has two squares of valuable veneer, each measuring $25$ units by $25$ units.
- One piece he cut, in the manner shown in our illustration, in four parts that will form two squares,
- one $20$ units by $20$ units, and the other $15$ units by $15$ units.
- Simply join $C$ to $A$ and $D$ to $B$.
- How is he to cut the other square into four pieces that will form again two other squares, with sides in exact units,
- but not $20$ and $15$ as before?
$106$ - Dissecting the Moon
- In how large a number of pieces can this crescent moon be cut with five straight cuts of the knife?
- The pieces may not be piled or shifted after a cut.
$107$ - Dissecting the Letter E
- Can you cut this letter $\text E$ into only five pieces so that they will fit together to form a perfect square?
- All the measurements have been given so that there should be no doubt as to the correct proportions of the letter.
- In this case you are not allowed to turn over any piece.
$108$ - Hexagon to Square
- Can you cut a regular hexagon into $5$ pieces that will fit together to form a square?
$109$ - Squaring a Star
- This six-pointed star can be cut into as few as five pieces that will fit together to form a perfect square.
- To perform the feat in $7$ pieces is quite easy,
- but to do it in $5$ is more difficult.
- The dotted lines are there to show the true shape of the star, which is made of $12$ equilateral triangles.
$110$ - The Mutilated Cross
- Here is a regular Greek cross from which has been cut a square piece exactly equal to one of the arms of the cross.
- The puzzle is to cut what remains into four pieces that will fit together and form a square.
$111$ - The Victoria Cross
- Cut the cross shown into seven pieces that will fit together and form a perfect square.
- Of course, there must be no trickery or waste of material.
$112$ - Squaring the Swastika
- Cut out the swastika and then cut it up into four pieces that will fit together and form a square.
$113$ - The Maltese Cross
- Can you cut the star into four pieces and place them inside the frame so as to show a perfect Maltese cross?
$114$ - The Pirates' Flag
- Here is a flag taken from a band of pirates on the high seas.
- The twelve stripes represented the number of men in the band,
- and when a new man was admitted or dropped out a new stripe was added or one removed, as the case might be.
- Can you discover how the flag should be cut into as few pieces as possible so that they may be put together again and show only ten stripes?
- No part of the material may be wasted, and the flag must retain its oblong shape.
$115$ - The Carpenter's Puzzle
- A ship's carpenter had to stop a hole $12$ inches square,
- How did he cut it into only two pieces that would exactly fit the hole?
- The answer is based on the "step principle", as shown in the diagram.
- If you move the piece marked $B$ up one step to the left,
- This is very simple and obvious.
- But nobody has ever attempted to explain the general law of the thing.
- As a consequence, the notion seems to have got abroad that the method will apply to any rectangle where the proportion of length to breadth is within reasonable limits.
- This is not so, and I have had to expose some bad blunders in the case of published puzzles that were supposed to be solved by an application of this step principle,
- but were really impossible of solution.$^*$
- Let the reader take different measurements, instead of $9 \ \mathrm{in.}$ by $16 \ \mathrm{in.}$,
- and see if he [or she] can find other cases in which this trick will work in two pieces and form a perfect square.
$116$ - The Crescent and the Star
- Here is a little puzzle on the Crescent and the Star.
- Look at the illustration, and see if you can determine which is the larger, the Crescent or the Star.
- If both were cut out of a sheet of solid gold, which would be more valuable?
- As it is very difficult to guess by the eye,
- I will state that the outer arc is a semicircle;
- the radius of the inner arc is equal to the straight line $BC$;
- the distance in a straight line from $A$ to $B$ is $12$ units,
- and the point of the star, $D$, contains $3$ square units.