Plug It Up!
Suppose you are given a board with three holes cut out of it:
Your task: Create a three-dimensional "plug" that would fit exactly (i.e. fill the space) when slid through each of the holes.
- An isosceles triangle (base width = 2 inches and height = 2 inches)
- A square (side length = 2 inches)
- A circle (diameter = 2 inches)
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.