Input-Output Machine & Pattern Rules

Feed numbers into a function machine and figure out the hidden rule. Try single-step and two-step operations, predict outputs from a pattern table, and extend number sequences. All computation runs in your browser.

Difficulty

Try an example

?

Reference Guide

Function Machines

A function machine follows a rule that transforms every input the same way. If the rule is "+ 3" then 2 becomes 5, 7 becomes 10, and 100 becomes 103.

Try different inputs to see what comes out. Look for the pattern between what goes in and what comes out.

Two-Step Rules

Some machines chain two operations together. For example, "× 2 then + 1" means first multiply by 2, then add 1.

With input 5, the first step gives 10, and the second step gives 11. Order matters because × 2 then + 1 is different from + 1 then × 2.

Finding the Rule

Look at how each input relates to its output. Ask yourself "what do I do to the input to get the output?"

  • If 3 → 8 and 5 → 10, the rule is + 5
  • If 2 → 6 and 4 → 12, the rule is × 3
  • Test your guess with another pair to be sure

Number Patterns

A number pattern is a sequence where each number follows a rule. Find what changes from one number to the next, then predict what comes after.

  • 2, 5, 8, 11, __ → the rule is + 3, so 14 is next
  • 3, 6, 12, 24, __ → the rule is × 2, so 48
  • Subtract the first number from the second to find the step