by Robert Benjamin and Dave Youngs.
Introduction
I am indebted to Robert Benjamin, a scientist from the Los Alamos National Laboratory,
for A Touchy Situation. Bob first did this activity with his son when
his son was in kindergarten. Therefore, he feels that the activity is appropriate
for students at all grade levels. He also notes that the activity works best
if students use Cuisenaire® Rods. The flat edges on the Cuisenaire®
Rods keep them from rolling and their differing lengths are necessary in Part
1 of the puzzle. If Cuisenaire® Rods are not available, pencils of varying
lengths can be substituted.
A Touchy Situation has two parts. In the first part, students are challenged to place rods on a flat surface (no stacking allowed) in such a way that each rod touches every other rod in the arrangement. At first glance, students may think that it is possible to get many rods to touch. However, after working on the problem for awhile they will find that although it is easy to get three rods to touch, getting four rods (the maximum possible) is not so easy.
In Part 2, students must follow the same rules as in Part 1 (each rod must touch every other rod in the arrangement), but this time they are allowed to stack the rods. At this point, you might want to challenge students to predict how many rods they think they can get to touch. In Bob's experience they often predict ten or more, and are surprised when they find that the maximum number of rods they can get to touch is much less.
Students who solve this puzzle early can be challenged to find (and sketch) multiple solutions for four, five, and six rods. They can also be challenged to think of additional solutions if one of the rods were flexible and could be bent.
Have fun and good luck!