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Mathematical Games of Martin Gardner Part 2

April is Mathematics and Statistics Awareness Month (MSAM) and we are continuing with our weekly nod to recreational mathematics inspired by “Mathematical Games,” the Scientific American columns authored by Martin Gardner from 1956-1981. This week’s puzzle features the contact number.

Four spheres arranged so each is touching the other three.

In this image, each sphere is in contact with the other three.

A contact number, which is akin to the “kissing number,” is the finite number of an object, often a sphere but not always, arranged in such a way that one is in contact with, or kisses, all others.

An example can be found in the arrangement of the four spheres shown to the right. Three are placed in a triangular formation on a plane while the fourth is nestled on top so that each sphere is touching the other three.

There are many objects that can be used for this game, but the one we’re going to use this week is the rod. This one is very much a hands-on 3-D experiment and the “rods” can be anything from pencils to straws.

This week’s puzzle: Can 6 rods be arranged in such a way that each is touching the other 5?

Last week’s puzzle was an example of tessellation, where polygons or other shapes can be arranged on a plane so that there are no gaps or overlaps between them. Our example was the rep-tile, a shape that is created by combining smaller replicas of that shape.

The solution to last week’s puzzle involving rep-tiles is below. The pieces are slightly separated so you can see how they fit together to form a larger replica of the original tile.

Answer to last week’s puzzle. You can see here how the pieces fit together to form a replica of the original tile.

As with last week, this week’s solution will appear in next week’s post. If you take part in any mathematical activities during the month of April, be sure to use #MathStatMonth for posts on social media. Good luck and share your experience with us in the comments!

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