Concept 6 of 7
Who Has What: One Clue Can Settle Two
Today's big idea
With two people and two things, one no names both of them.
With two people and two things, ruling one out of one thing fixes the other.
How it works
👀 What's going on?
Two friends, two things, and only one sentence telling you anything. It feels like too little to go on, and it is exactly enough.
💡 Here's the trick
Look at the table above. Amy and Bina have a cat and a dog between them, and the only clue is that Amy does not have the dog. Cross that box out. Amy is left with the cat, and because only one thing is left over, Bina must have the dog. One clue filled in both rows.
🪄 How to do it
- 1.Draw the names down the side and the things across the top, as the table above does.
- 2.Cross out the box the clue rules out.
- 3.Whatever is left with nowhere else to go belongs to the person who has a space left.
✍️ Try it
Ravi and Sara have a red bag and a blue bag, and Sara's is not red. Who has which? Then Anu and Dev play chess and cricket, and Dev does not play chess.
Sara's is not red, so Sara has the blue bag and Ravi has the red one. Dev does not play chess, so Dev plays cricket and Anu plays chess.
⚠️ Watch out
You might be thinking a clue about one person tells you nothing about the other. With only two people and two things it tells you everything, because ruling one out leaves the other no choice.
🌟 Why this matters
Working out what must be true from what cannot be is how you find a missing shoe or a misplaced book. Ruling things out is often faster than searching.
Exam tip: Cross boxes out on paper rather than trying to hold them in your head.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Tara and Uma have a book and a ball. Tara does not have the book. What does Uma have?”
- 1
Cross the forbidden box
Tara and book is out.
- 2
Read Tara's row
Only the ball is left, so Tara has that.
- 3
Uma has no choice
One clue named both, because there were only two of each.
- 4
Answer ✓
the book
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Cross out what the clue forbids, then read what is left.
TWO BY TWO · ROUND 1 OF 3
Step 1 · which box do you cross?
Quick check
✅ VERIFICATION
Meera and Nita own a bike and a scooter. Meera does not own the bike. What does Nita own?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Put the Steps in Order
Find the step with nothing before it, then follow the chain.