Concept 6 of 8
Who Has What: Three Names and a Grid
Today's big idea
Every tick clears the rest of its row and its column, not just the row.
A confirmed match rules out the rest of that person's row and that item's column.
How it works
👀 What's going on?
Three people and three things will not fall out of a single clue. You need two, and you need somewhere to keep track, because holding six possibilities in your head goes wrong fast.
💡 Here's the trick
Look at the grid above. Ravi, Sara and Tom own a cat, a dog and a fish. Sara owns the fish, so tick that box and cross out the rest of Sara's row and the fish column. Ravi does not own the dog, and the fish has gone, so Ravi owns the cat. Tom takes what is left.
🪄 How to do it
- 1.Draw the three names against the three things, as the grid above sets them out.
- 2.Tick what a clue confirms, then cross out the rest of that row AND that column.
- 3.Keep going until some row has only one box standing.
✍️ Try it
Amy, Bina and Cara study art, maths and music. Bina studies maths, and Amy does not study art. Who studies what? Then check your answer against both clues.
Bina takes maths, so cross maths off the others. Amy is not art and not maths, so Amy studies music. Cara is left with art. Both clues hold, so the grid is solved.
⚠️ Watch out
You might be thinking a tick only clears its own row. It clears the column too. Once Bina has maths, nobody else can, and forgetting that leaves the puzzle looking unsolvable.
🌟 Why this matters
Timetables, seating plans and rotas are all built by ruling out until one option stands. The grid is just a way of not losing your place.
Exam tip: Cross out a whole row and column with every tick, before reading the next clue.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Leo, Mia and Nia have an apple, a pear and a plum. Mia has the plum. Leo does not have the apple. What does Nia have?”
- 1
Tick Mia on the plum
That clears the rest of Mia's row AND the plum column.
- 2
Place Leo
Not the apple, and the plum has gone, so Leo takes the pear.
- 3
Nia takes what is left
Only the apple remains.
- 4
Answer ✓
the apple
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Every tick clears its row AND its column.
THREE BY THREE · ROUND 1 OF 3
Step 1 · what does that tick clear?
Quick check
✅ VERIFICATION
Ram, Sita and Om have a pen, a book and a ruler. Om has the book. Ram does not have the pen. What does Sita have?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Order the Steps
Ask what each loose step needs, and the order settles itself.