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Mathematics LibreTexts

2.8: Exploration

  • Page ID
    10361
  • [ "article:topic", "authorname:mmanes" ]

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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?

    onedot-300x87.png

    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.

    threedots-300x91.png

    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 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!