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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
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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 “AZ” the perpendicular
side is labelled “AY” and the hypotenuse is labelled “AX”.
Shape B, is a right angle triangle with a base 5 units long and a
perpendicular side 2 units long, the base is labelled “BZ” the perpendicular
side is labelled “BY” and the hypotenuse is labelled “BX”.
Shape C is a keyed box with 6 edges, edge 1 is labelled “CZ” and is 2
units long. Edge 2 is connected and perpendicular to edge “CZ”, is 2 units long
and is labelled “CY”. Edge 3 is perpendicular to and connected to edge “CY”, is
parallel and directly opposite to edge “CZ”, on opposite ends of edge “CY” from
“CZ”, is 1 unit long and is labelled “CX”. Edge 4 is perpendicular to and
connected to edge “CX”, is parallel to edge “CY”, on opposite ends of edge “CX”
from “CY”, is 3 units long and is labelled “CW”. Edge 5 is perpendicular to and
connected to edge “CW”, is parallel to edge “CX”, is parallel to and directly
opposite to edge “CZ”, on opposite ends of edge “CW” from “CX”, is 1 unit long
and is labelled “CV”. Edge 6 is perpendicular to and connected to edge “CV” and
is perpendicular to and connected to edge “CZ”, is parallel to and directly
opposite to edges “CW” and “CY”, on opposite end of edge “CV” from “CW” the
opposite end of edge “CZ” from “CY”, is 5 units long and is labelled “CU”.
Shape D is a keyed box with 6 edges, edge 1 is labelled “DZ” and is 2
units long. Edge 2 is connected and perpendicular to edge “DZ”, is 3 units long
and is labelled “DY”. Edge 3 is perpendicular to and connected to edge “DY”, is
parallel and directly opposite to edge “DZ”, on opposite ends of edge “DY” from
“DZ”, is 1 unit long and is labelled “DX”. Edge 4 is perpendicular to and
connected to edge “DX”, is parallel to edge “DY”, on opposite ends of edge “DX”
from “DY”, is 2 units long and is labelled “DW”. Edge 5 is perpendicular to and
connected to edge “DW”, is parallel to edge “DX”, is parallel to and directly
opposite to edge “DZ”, on opposite ends of edge “DW” from “DX”, is 1 unit long
and is labelled “DV”. Edge 6 is perpendicular to and connected to edge “DV” and
is perpendicular to and connected to edge “DZ”, is parallel to and directly
opposite to edges “DW” and “DY”, on opposite end of edge “DV” from “DW” the
opposite end of edge “DZ” from “DY”, is 5 units long and is labelled “DU”.

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
“CY” at the top. Shape D is positioned on top of Shape C with edge “DW” against
edge “CY”, edge “DX” against edge “CX” and edge “DY” against edge “CW”. Shape A
fits to the left of these two shapes with edge “AY” against edges “CV” and
“DZ”. Shape B fits on top of these shapes with edge “BZ” against edge “DU”.
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
“CY” at the top. Shape D fits beside and over shape C with edge “DW” against
edge “CW” and edge “DX” against edge “CV”. Shape B fits to the left of these
shapes with edge “BY” against edge “DZ”. Shape A fits over these shapes with
edge “AZ” against edges “DU” and “CY”. 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?







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