This post is about a problem I learned about at Unsolved K-12, and was reminded of at Integer Sequences K-12. Both conferences were joint meetings of mathematicians and educators, organized by Gord Hamilton. Like several of my favorite problems from those conferences, this problem involved explorations on a lattice.
Here is the problem:
– You must get from the top left corner of an n by n lattice to the bottom left.
– Each step must take you in a straight line to a lattice point.
– Each line segment thus created must be longer than the previous one.
– Your path cannot cross itself.
For example, this is not a successful trip, as the player did not reach the destination:
The figures above were created by Gord Hamilton. When introducing the problem to students, he tells a version of the story about Theseus, the Minotaur, and Ariadne — thus the title of this post. You should make up your own story.