Concept 6 of 6
Machine Rules: Run the Machine Backwards
Today's big idea
Undo the last step first, then feed your answer forwards to check it.
Undo the last step first, swapping each operation for its opposite as you go back.
How it works
👀 What's going on?
Every machine question so far has handed you the input. A Class 5 paper hands you the output instead and asks what went in. You have to walk the machine in reverse.
💡 Here's the trick
Look at the machine above. It doubles, then adds 5, and 19 came out. Going backwards you undo the LAST step first, so take away 5 to reach 14. Then undo the doubling by halving, which gives 7. Feed 7 forwards to check: 14, then 19.
🪄 How to do it
- 1.Write the steps in the order the machine above performs them.
- 2.Start from the output and undo the last step first, swapping each step for its opposite.
- 3.Feed your answer forwards through the machine to check it lands on the output.
✍️ Try it
One halves then adds 9, and 14 came out. What went in? Another subtracts 3 then multiplies by 4, and 20 came out. What went in?
Undo the add 9 to reach 5, then undo the halving by doubling, giving 10. For the second, undo the multiply by 4 to reach 5, then undo the subtract 3 by adding, giving 8.
⚠️ Watch out
You might be thinking you undo the steps in the order they are written. You undo them backwards. Taking the first step away first is the single commonest mistake here, and it gives an answer that looks reasonable.
🌟 Why this matters
Working back from a finished result is how you check a bill or find where a mistake crept in. Any process you can run forwards you can usually walk back.
Exam tip: Feed your answer forwards to confirm it, because that catches a reversed order.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“A machine adds 6 then doubles the result. The output is 22. What was the input?”
- 1
Which step happened last?
The double, so undo that one first.
- 2
Undo it
22 divided by 2 gives 11.
- 3
Undo the other
11 minus 6 gives 5. Forwards it runs 5, 11, 22.
- 4
Answer ✓
5
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Undo the LAST step first, then check by running it forwards.
REVERSE RUNNER · ROUND 1 OF 3
Step 1 · which step do you undo first?
Quick check
✅ VERIFICATION
A machine multiplies by 3 then adds 4. The output is 25. What was the input?
⚡ Finish the activity above first to answer.
Keep going!