2.8: Exploration
- Page ID
- 10361
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Jay decides to play with a system that follows a 1←1 rule. He puts one dot into the right-most box. What happens?
Poindexter decides to play with a system that follows the rule 2←3.
- Describe what this rule does when there are three dots in the right-most box.
- Draw diagrams or use buttons or pennies to find the codes for the following numbers: $$1\; \text{through}\; 20, 24, 27, 30, 33, 36,\; \text{and}\; 39$$
- Can you find (and explain) any patterns?
Repeat problem 45 for your own rule. Choose two numbers \(a \neq 1\) and 
. For each of the numbers
\[1\; \text{through}\; 20, 24, 27, 30, 33, 36,\; \text{and}\; 39 \nonumber \]
figure out the \(a \leftarrow b\) code. Look for patterns, and explain them if you can!