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

Question

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."