Logical reasoning · lesson 25 of 30 · free

Input–output machines — Logical reasoning for kids

A machine changes its input step by step: it may move the smallest number to the front each time, or multiply and add. Find the rule, then write each step on its own line until you reach the step asked for.

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How to think it through

One step, one line — “write the whole list after each step — never skip a step in your head”

  1. Read the rule carefully: what moves (or changes) in each step?
  2. Write the list (or number) after step 1, step 2, step 3 … each on a new line.
  3. Stop at the step asked and read the answer.

Use it for: Input–output and machine questions in aptitude tests, and the idea of an algorithm in coding.

Worked example: A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 45 12 78 33 91 27. After step 2, what is the 3rd number from the left? → 45

  1. Step 1: 12 45 78 33 91 27.
  2. Step 2: 12 27 45 78 33 91 — the 3rd number is 45.

Check: After 2 steps the two smallest (12, 27) are in front, the rest keep their order ✓

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✓ Written and checked by the TalentJR team · Updated 27 Oct 2026 · How we make our lessons

✏️ Practice

Work it out in your head or on paper, then tap your answer — or type it and press Check. Stuck? Press “Show me how”.

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🏁 Lesson 25 test

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🖨️ Input Output Reasoning Worksheet

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