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Topic: puzzel.
Replies: 1   Last Post: Sep 20, 1994 4:22 PM

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 keng@dspace.demon.co.uk Posts: 1 Registered: 12/6/04
puzzel.
Posted: Sep 16, 1994 10:39 AM

Geometry Puzzle

Parameters:

This puzzle is comprised of 2 equal right angle triangles made from 4 identical
shapes. The form of each shape is:
Shape A, is a right angle triangle with a base 8 units long and a
perpendicular side 3 units long, the base is labelled ÃÂAZÃÂ the perpendicular
side is labelled ÃÂAYÃÂ and the hypotenuse is labelled ÃÂAXÃÂ.
Shape B, is a right angle triangle with a base 5 units long and a
perpendicular side 2 units long, the base is labelled ÃÂBZÃÂ the perpendicular
side is labelled ÃÂBYÃÂ and the hypotenuse is labelled ÃÂBXÃÂ.
Shape C is a keyed box with 6 edges, edge 1 is labelled ÃÂCZÃÂ and is 2
units long. Edge 2 is connected and perpendicular to edge ÃÂCZÃÂ, is 2 units long
and is labelled ÃÂCYÃÂ. Edge 3 is perpendicular to and connected to edge ÃÂCYÃÂ, is
parallel and directly opposite to edge ÃÂCZÃÂ, on opposite ends of edge ÃÂCYÃÂ from
ÃÂCZÃÂ, is 1 unit long and is labelled ÃÂCXÃÂ. Edge 4 is perpendicular to and
connected to edge ÃÂCXÃÂ, is parallel to edge ÃÂCYÃÂ, on opposite ends of edge ÃÂCXÃÂ
from ÃÂCYÃÂ, is 3 units long and is labelled ÃÂCWÃÂ. Edge 5 is perpendicular to and
connected to edge ÃÂCWÃÂ, is parallel to edge ÃÂCXÃÂ, is parallel to and directly
opposite to edge ÃÂCZÃÂ, on opposite ends of edge ÃÂCWÃÂ from ÃÂCXÃÂ, is 1 unit long
and is labelled ÃÂCVÃÂ. Edge 6 is perpendicular to and connected to edge ÃÂCVÃÂ and
is perpendicular to and connected to edge ÃÂCZÃÂ, is parallel to and directly
opposite to edges ÃÂCWÃÂ and ÃÂCYÃÂ, on opposite end of edge ÃÂCVÃÂ from ÃÂCWÃÂ the
opposite end of edge ÃÂCZÃÂ from ÃÂCYÃÂ, is 5 units long and is labelled ÃÂCUÃÂ.
Shape D is a keyed box with 6 edges, edge 1 is labelled ÃÂDZÃÂ and is 2
units long. Edge 2 is connected and perpendicular to edge ÃÂDZÃÂ, is 3 units long
and is labelled ÃÂDYÃÂ. Edge 3 is perpendicular to and connected to edge ÃÂDYÃÂ, is
parallel and directly opposite to edge ÃÂDZÃÂ, on opposite ends of edge ÃÂDYÃÂ from
ÃÂDZÃÂ, is 1 unit long and is labelled ÃÂDXÃÂ. Edge 4 is perpendicular to and
connected to edge ÃÂDXÃÂ, is parallel to edge ÃÂDYÃÂ, on opposite ends of edge ÃÂDXÃÂ
from ÃÂDYÃÂ, is 2 units long and is labelled ÃÂDWÃÂ. Edge 5 is perpendicular to and
connected to edge ÃÂDWÃÂ, is parallel to edge ÃÂDXÃÂ, is parallel to and directly
opposite to edge ÃÂDZÃÂ, on opposite ends of edge ÃÂDWÃÂ from ÃÂDXÃÂ, is 1 unit long
and is labelled ÃÂDVÃÂ. Edge 6 is perpendicular to and connected to edge ÃÂDVÃÂ and
is perpendicular to and connected to edge ÃÂDZÃÂ, is parallel to and directly
opposite to edges ÃÂDWÃÂ and ÃÂDYÃÂ, on opposite end of edge ÃÂDVÃÂ from ÃÂDWÃÂ the
opposite end of edge ÃÂDZÃÂ from ÃÂDYÃÂ, is 5 units long and is labelled ÃÂDUÃÂ.

Placement of Shapes:

To form this puzzle the above shapes must be placed in 2 separate
configurations. Both configurations occupy the same area and have the same
shape (a right angle triangle).
Configuration 1. Shape C is in the bottom right hand corner with edge
ÃÂCYÃÂ at the top. Shape D is positioned on top of Shape C with edge ÃÂDWÃÂ against
edge ÃÂCYÃÂ, edge ÃÂDXÃÂ against edge ÃÂCXÃÂ and edge ÃÂDYÃÂ against edge ÃÂCWÃÂ. Shape A
fits to the left of these two shapes with edge ÃÂAYÃÂ against edges ÃÂCVÃÂ and
ÃÂDZÃÂ. Shape B fits on top of these shapes with edge ÃÂBZÃÂ against edge ÃÂDUÃÂ.
This will form a solid right angle triangle that is 13 units on the base 5
units on the perpendicular and 13.9 units on the hypotenuse.
Configuration 2. Shape C is in the bottom right hand corner with edge
ÃÂCYÃÂ at the top. Shape D fits beside and over shape C with edge ÃÂDWÃÂ against
edge ÃÂCWÃÂ and edge ÃÂDXÃÂ against edge ÃÂCVÃÂ. Shape B fits to the left of these
shapes with edge ÃÂBYÃÂ against edge ÃÂDZÃÂ. Shape A fits over these shapes with
edge ÃÂAZÃÂ against edges ÃÂDUÃÂ and ÃÂCYÃÂ. This forms a right angle triangle that
is 13 units at the base, 5 units on the perpendicular, 13.9 units on the
hypotenuse and with a hole of 1 unit square in the centre.

QUESTION:

My puzzle to yourselves is why does configuration 2 have a hole in it
and not configuration 1 when they are the same size and shape? Where does the
matter or hole in configuration 2 come from? Why do the two configurations not
have different dimensions?

Date Subject Author
9/16/94 keng@dspace.demon.co.uk
9/20/94 Richard Rognlie