Concept 6 of 7
Who Has What: A Clue That Rules Out Two
Today's big idea
Spend the negative clues first, because one can cross two boxes at once.
A negative clue that names two options clears two boxes in one sentence.
How it works
👀 What's going on?
Four names and four things give sixteen boxes, and a paper will not hand you four tidy clues. One of them will say what somebody does NOT do, twice over, in a single breath.
💡 Here's the trick
Look at the grid above. Amy plays neither tennis nor chess, which crosses two boxes at once. Bina plays hockey, so tick it and clear that row and column. Amy is now left with badminton alone. Cara does not play tennis, so Cara takes chess, and Dia is left with tennis.
🪄 How to do it
- 1.Read every clue before ticking anything, as the grid above starts with a double negative.
- 2.Spend the negative clues first, because they cost nothing and shrink the grid fastest.
- 3.Tick what is forced, clear the row and column, then read the clues again from the top.
✍️ Try it
With those four clues, who plays chess? And who is left with tennis?
Cara is not tennis, and hockey and badminton have gone to Bina and Amy, so Cara plays chess. Nothing is left for Dia but tennis, and no clue ever mentioned Dia at all.
⚠️ Watch out
You might be thinking a clue naming nobody new is wasted. A negative clue that names two things is the strongest one on the page, because it removes two boxes for the price of one sentence.
🌟 Why this matters
Rotas, seating plans and fixture lists are all built this way, from constraints rather than instructions. The last person is usually named by nothing at all. Working out what must be true from what cannot be is the whole skill.
Exam tip: Spend every negative clue before you hunt for a positive one.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Three boxes hold a red, a blue and a green ball. Box 1 is not red or green. Box 2 is green. Which ball is in Box 1?”
- 1
Spend the negative first
One sentence crosses two colours off Box 1 at once.
- 2
Place the positive
Box 2 holds green, so green is gone.
- 3
Only one colour is left
Box 1 is not red or green, so it must be blue.
- 4
Answer ✓
blue
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Spend the negative clues first. They clear two boxes each.
FOUR BY FOUR · ROUND 1 OF 3
Step 1 · how much does that one sentence do?
Quick check
✅ VERIFICATION
P, Q, R and S like red, blue, green and yellow. P likes neither red nor blue. Q likes blue. R likes red. S likes yellow. What does P like?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Order the Steps
Build the chain from what links, then test whatever is left over.