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:
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
figure out the code. Look for patterns, and explain them if you can!