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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:
\[1\text{ through }20, 24, 27, 30, 33, 36, \text{ and }
39\]
3. Can you find (and explain) any patterns?
Problem 46
Repeat problem 45 for your own rule. Choose two numbers $a \neq 1$ and $b$. For each of the numbers
\[1\text{ through }20, 24, 27, 30, 33, 36, \text{ and }
39,\]
figure out the $a \leftarrow b$ code. Look for patterns, and explain them if you can!
