Multipaths:

Find the total number of pathways from one corner of a 7×7 grid to another.  Remember: you can only move toward your goal – you can’t move backward or to the left.

On your assignment, show the total number of paths to each intersection, not just the endpoint.

Below the grid, write one paragraph about the patterns you notice in the grid.

Write up your solution to the Tower of Hanoi problem.

Include:

• A table showing the minimum number of moves for 1-10 discs
• A pattern or formula for determining the number of moves for any number of discs.
• An explanation or theory about how the formula/rule relates to the actual way the discs move. (about one paragraph)

The Switching Places Problem – part II

 

For the next time we meet (December 4th), prepare a report that answers the following questions.  You can use diagrams and tables to supplement what you say in words.  It does not have to be any length in particular, as long as you answer the questions thoroughly.

1.  What is the relationship between the number of slides and the number of jumps?  What patterns do you notice?  How are these patterns related to the actual situation?

2.  For any number of pairs of people, how many slides are there?

3.  For any number of pairs of people, how many jumps are there?

* Bonus: How many consecutive slides or jumps are there?  Why?

** Bonus: What patterns do you notice in who moves when? (the A/B pattern)

For next time type up a one-page description of your solution to the CUTE/WILD problem. Your reasoning should be clear and easy to follow. Check for correct spelling and grammar.

Create your own circle problem according to the guidelines on the sheet I distributed.  I won’t see you for 3 weeks.  When you bring in your circle puzzle, bring a “clean” copy and a copy with the answers (work shown).  Use Geometer’s Sketchpad as a drawing tool to create the puzzle, but use the rules you know to solve it.