Math Forum - Problem of the Week

Munching Bugs

Sam the Chameleon really loves math. He uses math to help him find the bugs he likes to eat. When looking for a bug at a particular point, Sam moves along the x-axis to reach the point's x coordinate and then sticks out his long tongue (up or down) to reach the point's y coordinate.

Use this applet and click on any point to see Sam in action:

One day Sam decides he will use a math rule to help him choose which bugs to eat: he will always stick his tongue out 1 more unit than twice the distance that he walked to find the bug. [Sam always starts at (0, 0)].

  1. Name 3 points Sam could reach by following his rule.
  2. Name 3 points Sam could not reach by following his rule.
  3. Explain Samís rule using one or more equations.

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