Concept 1 of 7
Ranking: Tallest to Shortest, Heaviest to Lightest
Today's big idea
Turn every comparison into an arrow, then snap the arrows into one chain.
A > B and B > C join up into the single order A > B > C.
How it works
👀 What's going on?
A ranking puzzle never hands you the order. It hands you a few comparisons and expects you to build the order out of them yourself.
💡 Here's the trick
Look at the chain above. A is taller than B becomes A > B, and B is taller than C becomes B > C. Line those two up and they join into A > B > C, the full order with the tallest first. Every fact is one link, and the links snap together.
🪄 How to do it
- 1.Rewrite each fact as a > arrow, the way the picture above does.
- 2.Snap the arrows together wherever they share a name.
- 3.Read the finished chain off, biggest first.
✍️ Try it
P is taller than Q. R is taller than P. S is shorter than Q. Put all four in order, tallest first.
P > Q and R > P snap together as R > P > Q. S is shorter than Q, so S goes on the end, giving R, P, Q, S. Start from whichever pair shares a name, because that is where the chain begins.
⚠️ Watch out
You might be thinking a ranking puzzle only ever compares one thing. Some give you two, such as age and height. Keep a separate chain for each, because the tallest child is not automatically the oldest.
🌟 Why this matters
Sports tables, class positions and race results are all built out of comparisons like these. Turning sentences into arrows is what stops a page of facts becoming a muddle.
Exam tip: Write the arrows down rather than reasoning in your head, because one reversed arrow flips the entire order.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“A > B, C < B. Order from tallest.”
- 1
Translate
A > B. B > C (since C < B).
- 2
Stack arrows
A > B > C.
- 3
Answer ✓
A, B, C
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Box R is heavier than P. P is heavier than Q. Tap the items in order: heaviest → lightest.
RANK · ROUND 1 OF 3
Quick check
✅ VERIFICATION
M is heavier than N. L is heavier than M. Order them from heaviest to lightest.
⚡ Finish the activity above first to answer.
Keep going!
Up next: Odd One Out
Three same property. One doesn't fit.