9 Exploration
Problem 44
Jay decides to play with a system that follows a 1←1 rule. He puts one dot into the right-most box. What happens?
Problem 45
Poindexter decides to play with a system that follows the rule 2←3.
1. Describe what this rule does when there are three dots in the right-most box.
2. Draw diagrams or use buttons or pennies to find the codes for the following numbers:
![\[1\text{ through }20, 24, 27, 30, 33, 36, \text{ and } 39\]](http://pressbooks.oer.hawaii.edu/mathforelementaryteachers/wp-content/ql-cache/quicklatex.com-cc63893e2c44d4f0b11b1e289bf64bea_l3.png "Rendered by QuickLaTeX.com")
3. Can you find (and explain) any patterns?
Problem 46
Repeat problem 45 for your own rule. Choose two numbers 
and 
. For each of the numbers
![\[1\text{ through }20, 24, 27, 30, 33, 36, \text{ and } 39,\]](http://pressbooks.oer.hawaii.edu/mathforelementaryteachers/wp-content/ql-cache/quicklatex.com-b08275244501ed8f62f9e3cc0483fb45_l3.png "Rendered by QuickLaTeX.com")
figure out the 
code. Look for patterns, and explain them if you can!
