https://file.aiquickdraw.com/mathbot/file/1725988284855q0n3500k.jpg

The problem involves the concept of a "cyclic number system," often seen in modular arithmetic, specifically related to numbers divisible by 3. Here's how we can break it down:

### Question analysis:
- The image shows a sequence of numbers with some not divisible by 3.
- The task is to identify how far the first non-divisible by 3 number is from the rightmost number.

### Step-by-step breakdown:
1. **Given numbers**: \( \{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 \} \)
2. **Non-divisible by 3**: Among the numbers, those divisible by 3 are \( \{ 0, 3, 6, 9 \} \). The non-divisible ones are \( \{ 1, 2, 4, 5, 7, 8 \} \).
3. **First non-divisible by 3**: Referring to the diagram and arrows, the first number that is not divisible by 3 appears at position 1 (to the left).
4. **The third place**: The question asks for the third place that is non-divisible by 3, which occurs at 5.

### Checking the options:
- The correct ratio to identify the sequence depends on how many divisible numbers come before the specified non-divisible one.

Given the context, I would need more information from you to ensure the accuracy of the sequence interpretation

What is the ratio of the third number in the sequence that is not divisible by 3 to the total number of options?

Explore how to find the ratio of numbers that are not divisible by 3 in a sequence. This problem involves understanding modular arithmetic and applying divisibility rules, suitable for middle school students.

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