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.

Our first problem of the year is the Canoe Problem that we started in class.  Your homework is to solve the problem up to 10 people (5 on each side).  You must show your solution to 10 people using notation or diagrams of your choice.  Then write at least half a page about patterns and strategies that you noticed while solving these.  You can also predict how the pattern will proceed.  Bring signed contracts to class next week for me to collect.  You should have a seminar folder by then and it should be well stocked with loose graph paper. 

Give your message encrypted with an A-multiplier and B-shift to a classmate.  You may use either paper & pencil or an excel spreadsheet to decrypt each others’ messages.

Also, write a seminar reflection for the year and email it to me at achaney@lrei.org

Think about one problem you have worked on this year that you found particularly satisfying.  Describe the process you went through.  What worked?  What felt good? What was difficult?  What does this say about your problem solving style?  How do you think they year went for you overall?

I used an a-multiplier of 5.  This time, I didn’t leave you spaces for the words.  Extra credit if you can tell me who said this!

9    23    15    23    18    4    19    20    25    18    22    8    21

19    18    22    14    25    20    19    12    25    15    22    19    23

18    23    4    21    23    1    12    20    12    25    5    13    17