Ana’s Math Blog
Announcements, assignments and links

 Due after winter break:Play hex-7 at least three times with a parent.  Then read about the game’s strategy on mazeworks.  At the end of the pages about hex strategy, there are three problems.  In each one, white makes the next move that will force a win.  Solve two of these puzzles for homework.  Bring your solutions to class.

Tower of Hanoi

Use this applet to find the number of moves (M) it would take for any number of discs (D).

Write one page describing your strategy and how it connects to the formula.  Use diagrams if you need them.  Your writing should be proofread and all diagrams must be made neatly.

Do patterns D, E and F for homework.  For each pattern, copy the first three stages, draw the 4th and 5th, and write about what you notice.  Thn create a table for stages 1-10 and write a formula to describe the number of dots at any stage.  Prove it works by calculating the number of dots at the 100th stage.

Finish solving the “Bats Flying Backwards” problem.

Your write-up of the solution is due when I see you next week.

It must include:

• A table up to 20 rows
• Rules (2 or 3) that work for generating the numbers in each row
• Explainations of each rule
• Diagrams explaining each of the methods used
• An explanation of why you can’t use the same method or rule each time.

Additionally, your write-up must be neat, have a complete heading, and be checked for grammar and spelling.  All diagrams must be done with a ruler (or on the computer).  All writing must be typed.

(DUE  in 2 weeks - Oct. 17th)Answer the following questions.  Use complete sentences and provide explanations and illustrations when necessary.  Be thorough and neat.

1.  How is the number of slides related to the number of people?  Why?
2. How is the number of jumps related to the number of people?  Why?
3. Can you have more than one slide in a row?  Why/why not?
4. Why does the number of consecutive jumps increase and then decrease as the “people” move from one side to the other?
5. How is the largest number of consecutive jumps possible related to the number of people?
6. Adding a pair of people when there are only 2 pairs to begin with adds fewer moves than adding a pair of people when there are already 10 pairs.  Why?
7. How many moves will it take to have 100 pairs of people switch place?  Show your work.