
# 1.8: 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.

1. Draw diagrams or use buttons or pennies to find the codes for the following numbers: $$1\; \text{through}\; 20, 24, 27, 30, 33, 36,\; \text{and}\; 39$$
2. Can you find (and explain) any patterns?

## Problem 46

Repeat problem 45 for your own rule. Choose two numbers $$a \neq 1$$ and . For each of the numbers

$1\; \text{through}\; 20, 24, 27, 30, 33, 36,\; \text{and}\; 39$

figure out the $$a \leftarrow b$$ code. Look for patterns, and explain them if you can!

1.8: Exploration is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Michelle Manes via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.