A Tough Grid-Moving Puzzle (ESSAY!)

Take a walk on an 8×8 grid of squares. Step only left, right, up and down one unit at a time (no diagonal steps, no leaps over intermediate cells) and return to start. Then I bet …

1) You took an odd number of right steps and an odd number of up steps, and that these odd counts of steps were not equal.
2) You traced a polygon of area 31

In this essay we go through the tricky machinations to see why these claims must be true.

Grid-Moving Puzzle

• ON-LINE SHORT COURSES!

  QUADRATICS, Permutations and Combinations, EXPLODING DOTS, and more!

  Written for educators - and their students too! - this website, slowly growing, takes all the content Tanton has developed in his books, videos, and workshops, and organizes it into short, self-contained, and complete, curriculum units proving that mathematics, at all points of the school curriculum, can be joyous, fresh, innovative, rich, deep-thinking, and devoid of any rote doing! Let's teach generations of students to be self-reliant thinkers, willing to flail and to use their common sense to "nut their way" through challenges, to assess and judge results, and to adjust actions to find success. (Great life skills!)

  CHECK OUT: www.gdaymath.com

• Books

  • Thinking Mathematics! (TEN VOLUMES)
  • Solve This: Mathematical Activities for Students and Clubs
  • Encyclopedia of Mathematics
  • Geometry I & II

• Get in touch

  Email: tanton.math@gmail.com