Concept 4 of 5
Number Detective
Today's big idea
Fix the digit you are certain of first, then let the clues fill the others.
A right digit in the wrong place is the slip, so name each place aloud.
How it works
👀 What's going on?
A number is described rather than given. You are told things about its digits and asked to name it. The order you take those clues in decides whether it is easy or a mess.
💡 Here's the trick
Look at the clues above. One of them usually pins a digit down exactly, and that is the one to use first. Once a digit is fixed, the clues that depend on it stop being guesses and become simple sums.
🪄 How to do it
- 1.Read every clue in the list above before writing anything.
- 2.Start with the clue that fixes one digit on its own.
- 3.Use the remaining clues to work out the rest.
✍️ Try it
The tens digit is 4 and the ones digit is 3 less than the tens. Then: a two-digit number whose digits add to 9, where the tens digit is twice the ones.
Four take away three is one, so the number is 41. For the second, the digits must add to 9 with one being double the other, which gives 6 and 3, so the number is 63.
⚠️ Watch out
You might be thinking any clue is as good a starting point as another. Begin with a clue that leaves two possibilities open and you carry both of them through every step. Find the clue that pins something exactly and start there instead.
🌟 Why this matters
Narrowing possibilities down until only one survives is how any puzzle with clues works, from a crossword to a missing house number. Order of attack is most of it.
Exam tip: Write the tens and ones boxes on your paper and fill whichever one the clues fix first.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“The ones digit is 2, and the tens digit is 6 more than the ones digit. What is the number?”
- 1
Fix the sure digit
Ones digit = 2. 🔎
- 2
Use the next clue
Tens = 2 + 6 = 8.
- 3
Answer ✓
The number = 82
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Solve the clue that fixes one digit first, then fill the rest.
CLUE · ROUND 1 OF 3
Ones = 2, tens = 3 more than ones
What is the number?
Quick check
✅ VERIFICATION
A number is between 20 and 30, and its digits add to 7. What is the number?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Fractional-Spend Shopping
Split and take each piece, then combine.