Friday, September 14, 2007

Parable of Erin the Problem Solver

Perhaps you are familiar with a brain-teaser called the Konigsberg Bridge Problem. A Swiss mathematician named Euler developed a way of working with graph theory to "solve" the puzzle, but the sixth-grade math teacher posed it to his class anyways.

He drew a diagram of the two islands in the Preger River and the seven bridges. The students scribed their own versions on lined notebook paper and began trying to find a way to trace a path over all the bridges without crossing back.

All the students except one, that is. Some students briefly lifted their heads up from their work upon hearing the loud crumpling caused by Erin squishing and rolling up her pencilled-on-paper worksheet into a ball. Then she took a freshly-sharpened pencil and began stabbing away at the wrinkly paper orb.

After a few seconds she stopped, unravelled the paper wad, flattened it as best they could on their desk, and looked upon it smiling.

The pencil stabs had indeed traced a successful route, but a new bridge had been torn into the problem by the pokes of graphite. Without another bridge it was unsolvable.

Upon inspecting her solution the teacher was amazed but not amused by Erin's inelegant method.

The teacher returned to the front of the class where he graphed out the problem on the chalkboard, using Euler's technique. After all he couldn't just wad up an entire blackboard and stab away at it as Erin had done with her paper.

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