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Constructive Solid Geometry (CSG) Puzzle

What single object can slide exactly through each of the holes shown besides without leaving gaps ?

That is, the object must slip through each hole filling the hole completely.
 




The solution is as shown in figure besides.

When viewed normal to the green face (side view), it will appear a circle.

When viewed normal to the blue face (top view), it is a square, and

The front view will show a plus shape.

So what has this got to do with CAD...?
 




This object is the intersection of each of the outlines of the holes extruded along each of the three orthogonal axes. The plus shape is in turn made up of union of two rectangular blocks. This is called CSG or Constructive Solid Geometry.
 




If you have good woodworking skills and make one of these, probably from wood, please let me know and perhaps send me a copy.

You may take a cylindrical block of diameter 1 unit and height 1 unit and chisel it out at four places by, say, 0.3 units as shown in the animation on the right.

Also, Don't forget to make the base block with the three holes to test it.
 



The Purple Cube Puzzle

  • So U are doing CAD, CAM, CA...blah blah for around 5 years now.
  • And you are the most sought after CAD guy in your office.
  • And you have been good at geometry in general and CAD in particular since the 7th grade.

  • Fine !

    This one will make you look inwards.

    A stack of 27 cubes (3 x 3 x 3) was dipped in liquid purple color.

    Answer to yourself.....Quickly...

  • How many cubes now have only one face purple ?
  • How many cubes have two faces purple ?
  • How many cubes have three faces purple ?
  • How many cubes are uncolored ?

  •  



    Spot the difference Puzzle

    This one is a total timepass puzzle.

    ScreenShots of two AutoCAD sessions are here.

    You have to spot 10 differences betweeen the two AutoCAD pictures.
     
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