Question

Which rule would make all of these input-output pairs true?
input
Input Output Arrow
rule
Input Output Arrow
output


Input Output
6 4
44 23
9 5.5
4 3

Write 4.

Divide by 2, then add 1.

Subtract 2.

If even, subtract 2. If odd, add 5.

Answer 1

To determine a rule that applies to all the input-output pairs you've provided, we can analyze the relationships between each input and its corresponding output.

**Input-Output Pairs:**
1. 6 → 4
2. 44 → 23
3. 9 → 5.5
4. 4 → 3

Let's analyze each one based on potential rules that were suggested:

1. **Rule: Write 4.**
This rule does not apply as it simply would output "4" for every input.

2. **Rule: Divide by 2, then add 1.**
- For 6: (6/2) + 1 = 3 + 1 = 4 (True)
- For 44: (44/2) + 1 = 22 + 1 = 23 (True)
- For 9: (9/2) + 1 = 4.5 + 1 = 5.5 (True)
- For 4: (4/2) + 1 = 2 + 1 = 3 (True)
This rule works for all pairs.

3. **Rule: Subtract 2.**
- For 6: 6 - 2 = 4 (True)
- For 44: 44 - 2 = 42 (False)
Thus, this rule does not apply.

4. **Rule: If even, subtract 2. If odd, add 5.**
- For 6 (even): 6 - 2 = 4 (True)
- For 44 (even): 44 - 2 = 42 (False)
- For 9 (odd): 9 + 5 = 14. (False)
Thus, this rule does not apply.

From this analysis, the rule that fits all the input-output pairs is:
**"Divide by 2, then add 1."**