Concept 7 of 7
Find the Rule
Today's big idea
Compare each In with its Out to find the single times-rule the machine uses.
2→10 and 3→15 both fit × 5, so that is the rule.
How it works
👀 What's going on?
A number goes into a machine and a new one comes out. The machine will not tell you what it does inside, but if you watch a few numbers go through, you can work out its secret rule.
💡 Here's the trick
Look at the In/Out table above. 2 comes out as 10, 3 comes out as 15, 4 comes out as 20. Each number going in is multiplied by 5 to get the number coming out. Once you spot the rule, you can work out any answer.
🪄 How to do it
- 1.Look at one in number and its out number.
- 2.Ask what you did to get from in to out: times 2, times 5, or times 10?
- 3.Check the same rule works for the other pairs, then use it.
✍️ Try it
In 2 → Out 20, In 3 → Out 30, In 5 → Out 50. What is the rule, and what does 6 give?
Each out is the in times 10, so the rule is × 10. Then 6 gives 6 × 10 = 60.
⚠️ Watch out
Check more than one pair. '2 → 10' on its own could be × 5 or + 8; the next pair, '3 → 15', tells you it is × 5.
🌟 Why this matters
Finding a hidden rule is the start of spotting patterns and thinking like a detective. It is a skill you will use in every puzzle.
Exam tip: Try the times tables first — most machines multiply by 2, 5 or 10.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“In → Out: 2 → 10, 3 → 15, 4 → 20. What is the rule?”
- 1
Compare in with out
Each out is 5 times its in.
- 2
Check a second pair
3 × 5 = 15 ✓, so it is not + 8.
- 3
Answer ✓
the rule is × 5
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Two pairs, not one. Then send your number through.
RULE SPOTTER · ROUND 1 OF 3
Step 1 · name the rule
Quick check
✅ VERIFICATION
In → Out: 2 → 10, 3 → 15, 4 → 20. What is the rule?
⚡ Finish the activity above first to answer.
Keep going!