Mar. 1, entry #6

I found a problem to work on (actually kindly given to me by Danny from a choice of 3)! I have only now begun to explore it with some more thought. So I will bring some more attention to it in my upcoming slogs. The problem is as follows: 

tiling
Work with 1 or 2 other students, and choose one of your group as the recorder. The recorder should keep a written record of his/her group's discussion of the problem below. Use the following headings to organize the discussion:
􏰂 Understand the problem. 
􏰂 Devise a plan.
􏰂 Carry out the plan.
􏰂 Look back.
􏰂 Acknowledge when, and how, you're stuck.
Suppose you have tiles that are 1 􏰁 2 rectangles, and you have a walk that is 2 􏰁 3 units long. There are three ways to tile your walk: three vertical tiles, one vertical tile followed by two horizontal tiles, or two horizontal tiles followed by one vertical tile.
How many di􏰀erent ways are there to tile a 2 􏰁 4 walk, or (indeed) a 2 􏰁 n walk (where n is some natural number)? Can you come up with a general procedure that works?
What happens if your tiles are 1 􏰁 3, and you have a walk that is 3 􏰁 n units long?

You can continue working on this problem at:

https://wwwcgi.cdf.toronto.edu/~heap/cgi-bin/Solvent/wiki.pl?Problem_Solving_Home_Page/WalkTilings
userid: sleuth
password: eureka

Hint 1, organize: Organize your counting according to what the orientation of the left-most tile is.    

I hope everyone had a great week! Keep on Sloggin'!