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Plug It Up!

Suppose you are given a board with three holes cut out of it:

  • An isosceles triangle (base width = 2 inches and height = 2 inches)
  • A square (side length = 2 inches)
  • A circle (diameter = 2 inches)
Your task: Create a three-dimensional "plug" that would fit exactly (i.e. fill the space) when slid through each of the holes.

Trying to figure out what this problem even means? First, think about the spatial-visualization problems involving FRONT, TOP, and SIDE views. And, consider this piece of wood that was sold on e-bay recently (had 3 bids and sold for $1.95) and build a single object that would "plug" each hole:

 


Hint: Think about shapes of objects that you use daily, especially in the morning.

 


Solution Commentary: Rather than give the answer, you might want to look at the playing pieces for the Triple Try Game.

Also, find and read Richard Jerrard/John Wetzel's "Universal Stoppers are Rupert" (College Mathematics Journal, March 2008, pp. 90-94).

In case you did not connect the hint, think about the variations on the shape of tubes of toothpaste or handcream.