Question

Which rules would make this input-output pair true?
input
11
rule
Input Output Arrow
?
Input Output Arrow
output
23
Could be a rule for this input-output pair Could not be a rule for this
input-output pair
Write 11.
Add 12.
Multiply by 2, then add 1.
If even, add 12. If odd, add 10.
Multiply by 3, then subtract 10.

Answer 1

To determine which rules could make the input-output pair of 11 leading to 23 true, we can evaluate each rule based on the operations it describes.

1. **Write 11**: This rule does nothing to the input. The output remains 11, so this cannot be true.

2. **Add 12**:
- Input: 11
- Output: 11 + 12 = 23
- This rule is valid.

3. **Multiply by 2, then add 1**:
- Input: 11
- Output: (11 * 2) + 1 = 22 + 1 = 23
- This rule is valid.

4. **If even, add 12. If odd, add 10**:
- Since 11 is odd, we add 10.
- Input: 11
- Output: 11 + 10 = 21, not 23.
- This rule is not valid.

5. **Multiply by 3, then subtract 10**:
- Input: 11
- Output: (11 * 3) - 10 = 33 - 10 = 23
- This rule is valid.

Based on these evaluations, the rules that could make the input-output pair true are:

- Add 12
- Multiply by 2, then add 1
- Multiply by 3, then subtract 10

So, summarizing:
- **Could be a rule for this input-output pair**:
- Add 12
- Multiply by 2, then add 1
- Multiply by 3, then subtract 10

- **Could not be a rule for this input-output pair**:
- Write 11
- If even, add 12. If odd, add 10.