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

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

Write 4.

Divide by 2, then add 1.

Subtract 2.

Answer 1

Based on the input-output pairs provided, let's analyze them according to the suggested rules:

Input-Output Pairs Analysis:

1. For Input 6:

   • Output is 4.
   • If we subtract 2 from 6, we get 4 (6 - 2 = 4).

2. For Input 44:

   • Output is 23.
   • If we apply the divide rule: (44 / 2 = 22) + 1 gives us 23.

3. For Input 9:

   • Output is 5.5.
   • If we divide by 2, then add 1: (9 / 2 = 4.5) + 1 = 5.5.

4. For Input 4:

   • Output is 3.
   • Subtracting 2 from 4 yields 2. However, if we instead divide: (4 / 2 = 2) + 1 gives us 3.

Conclusion:

The best-fitting rule seems to be:

• If the input is even, divide by 2 and then add 1.
• If the input is odd, divide by 2, then add 1.

Final Rule:

Both even and odd inputs follow the rule of "divide by 2 then add 1," generating the outputs given.

So, the rule that applies to all the input-output pairs is: "Divide by 2, then add 1."