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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 ÃÂAZÃÂ the perpendicular side is labelled ÃÂAYÃÂ and the hypotenuse is labelled ÃÂAXÃÂ. Shape B, is a right angle triangle with a base 5 units long and a perpendicular side 2 units long, the base is labelled ÃÂBZÃÂ the perpendicular side is labelled ÃÂBYÃÂ and the hypotenuse is labelled ÃÂBXÃÂ. Shape C is a keyed box with 6 edges, edge 1 is labelled ÃÂCZÃÂ and is 2 units long. Edge 2 is connected and perpendicular to edge ÃÂCZÃÂ, is 2 units long and is labelled ÃÂCYÃÂ. Edge 3 is perpendicular to and connected to edge ÃÂCYÃÂ, is parallel and directly opposite to edge ÃÂCZÃÂ, on opposite ends of edge ÃÂCYÃÂ from ÃÂCZÃÂ, is 1 unit long and is labelled ÃÂCXÃÂ. Edge 4 is perpendicular to and connected to edge ÃÂCXÃÂ, is parallel to edge ÃÂCYÃÂ, on opposite ends of edge ÃÂCXÃÂ from ÃÂCYÃÂ, is 3 units long and is labelled ÃÂCWÃÂ. Edge 5 is perpendicular to and connected to edge ÃÂCWÃÂ, is parallel to edge ÃÂCXÃÂ, is parallel to and directly opposite to edge ÃÂCZÃÂ, on opposite ends of edge ÃÂCWÃÂ from ÃÂCXÃÂ, is 1 unit long and is labelled ÃÂCVÃÂ. Edge 6 is perpendicular to and connected to edge ÃÂCVÃÂ and is perpendicular to and connected to edge ÃÂCZÃÂ, is parallel to and directly opposite to edges ÃÂCWÃÂ and ÃÂCYÃÂ, on opposite end of edge ÃÂCVÃÂ from ÃÂCWÃÂ the opposite end of edge ÃÂCZÃÂ from ÃÂCYÃÂ, is 5 units long and is labelled ÃÂCUÃÂ. Shape D is a keyed box with 6 edges, edge 1 is labelled ÃÂDZÃÂ and is 2 units long. Edge 2 is connected and perpendicular to edge ÃÂDZÃÂ, is 3 units long and is labelled ÃÂDYÃÂ. Edge 3 is perpendicular to and connected to edge ÃÂDYÃÂ, is parallel and directly opposite to edge ÃÂDZÃÂ, on opposite ends of edge ÃÂDYÃÂ from ÃÂDZÃÂ, is 1 unit long and is labelled ÃÂDXÃÂ. Edge 4 is perpendicular to and connected to edge ÃÂDXÃÂ, is parallel to edge ÃÂDYÃÂ, on opposite ends of edge ÃÂDXÃÂ from ÃÂDYÃÂ, is 2 units long and is labelled ÃÂDWÃÂ. Edge 5 is perpendicular to and connected to edge ÃÂDWÃÂ, is parallel to edge ÃÂDXÃÂ, is parallel to and directly opposite to edge ÃÂDZÃÂ, on opposite ends of edge ÃÂDWÃÂ from ÃÂDXÃÂ, is 1 unit long and is labelled ÃÂDVÃÂ. Edge 6 is perpendicular to and connected to edge ÃÂDVÃÂ and is perpendicular to and connected to edge ÃÂDZÃÂ, is parallel to and directly opposite to edges ÃÂDWÃÂ and ÃÂDYÃÂ, on opposite end of edge ÃÂDVÃÂ from ÃÂDWÃÂ the opposite end of edge ÃÂDZÃÂ from ÃÂDYÃÂ, is 5 units long and is labelled ÃÂDUÃÂ.
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 ÃÂCYÃÂ at the top. Shape D is positioned on top of Shape C with edge ÃÂDWÃÂ against edge ÃÂCYÃÂ, edge ÃÂDXÃÂ against edge ÃÂCXÃÂ and edge ÃÂDYÃÂ against edge ÃÂCWÃÂ. Shape A fits to the left of these two shapes with edge ÃÂAYÃÂ against edges ÃÂCVÃÂ and ÃÂDZÃÂ. Shape B fits on top of these shapes with edge ÃÂBZÃÂ against edge ÃÂDUÃÂ. 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 ÃÂCYÃÂ at the top. Shape D fits beside and over shape C with edge ÃÂDWÃÂ against edge ÃÂCWÃÂ and edge ÃÂDXÃÂ against edge ÃÂCVÃÂ. Shape B fits to the left of these shapes with edge ÃÂBYÃÂ against edge ÃÂDZÃÂ. Shape A fits over these shapes with edge ÃÂAZÃÂ against edges ÃÂDUÃÂ and ÃÂCYÃÂ. 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?



