A woman visitor to the city entered a taxicab. No sooner was the door closed than the car leaped forward violently, and afterward went racing wildly along the street, narrowly missing collision with innumerable things. The passenger, naturally ... Read more of Beginners at Free Jokes.caInformational Site Network Informational
Privacy
Home Top Rated Puzzles Most Viewed Puzzles All Puzzle Questions Random Puzzle Question Search


THE DISSECTED TRIANGLE.

(Various Dissection Puzzles)
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?
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.


Answer:

Diagram A is our original triangle. We will say it measures 5 inches (or
5 feet) on each side. If we take off a slice at the bottom of any
equilateral triangle by a cut parallel with the base, the portion that
remains will always be an equilateral triangle; so we first cut off
piece 1 and get a triangle 3 inches on every side. The manner of finding
directions of the other cuts in A is obvious from the diagram.
Now, if we want two triangles, 1 will be one of them, and 2, 3, 4, and 5
will fit together, as in B, to form the other. If we want three
equilateral triangles, 1 will be one, 4 and 5 will form the second, as
in C, and 2 and 3 will form the third, as in D. In B and C the piece 5
is turned over; but there can be no objection to this, as it is not
forbidden, and is in no way opposed to the nature of the puzzle.










Random Questions

The Great Monad.
Various Dissection Puzzles
Dominoes In Progression.
Problems Concerning Games.
The Millionaire's Perplexity.
Money Puzzles
The Queen's Tour.
The Guarded Chessboard
The Christmas-boxes.
Money Puzzles
The Forsaken King.
The Guarded Chessboard
The Bag Of Nuts.
Money Puzzles
The Motor-garage Puzzle.
Moving Counter Problem
The Railway Station Clock.
Money Puzzles
Wilson's Poser.
Money Puzzles
The Queen's Journey.
The Guarded Chessboard
The Twelve Pennies.
Moving Counter Problem
The English Tour
MISCELLANEOUS PUZZLES
The Game Of Bandy-ball
PUZZLING TIMES AT SOLVAMHALL CASTLE
A Railway Muddle.
Moving Counter Problem