Concept 2 of 4
Ranking & Position: From-Left vs From-Right
Today's big idea
Adding a place from each end counts that child twice, so L + R − 1 = Total.
Counting from both ends double-counts one person, so subtract 1 to fix it.
How it works
👀 What's going on?
Your teacher lines the class up and calls the sixth child from the front. You count from the front and get one child, your friend counts from the back and gets another. The same person has two different numbers, and both are right.
💡 Here's the trick
Look at the row above. Every child has a place counted from the left and another counted from the right. Add those two numbers and you count that child twice, so the two places always come to the total plus one.
🪄 How to do it
- 1.Mark the two children named in the question on the row above.
- 2.Swap any right-hand place to a left-hand one using total minus place plus one.
- 3.Subtract the two left-hand places, then take one more off for the child.
✍️ Try it
In a row of 18 children, Kabir is 7th from the left, so what is his place from the right? Then: Meera is 9th from the left and 12th from the right in one row, so how many children stand in that row?
Kabir's place from the right is 18 − 7 + 1 = 12th. Meera gets counted twice, so the row holds 9 + 12 − 1 = 20 children.
⚠️ Watch out
You might be thinking you can add the two places to get the total. That counts the child in the middle twice. Take one off, so 6th from the left and 10th from the right is a row of 15, not 16.
🌟 Why this matters
Queues at the canteen, seats in a cinema row and places in a race all count from one end or the other. Once you can swap ends, you never have to recount the whole line.
Exam tip: Write the total under the row first, because almost every rank question leans on it.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“In a row of 24 children, Sara is 7th from the LEFT and Tara is 9th from the RIGHT. How many between them?”
- 1
Convert Tara's rank to from-left
24 − 9 + 1 = 16
- 2
Between formula
Between = later − earlier − 1 = 16 − 7 − 1
- 3
Compute
8
- 4
Answer ✓
8 children between
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Make Sam stand 3th from the left and 6th from the right. Tap to add children on each side.
POSITION · ROUND 1 OF 3
Sam is now 1 from left · 1 from right
Quick check
✅ VERIFICATION
In a row of 20 children, Anu is 8th from the left and Bina is 6th from the right. How many children are between them?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Day Calculation
Divide by 7, keep the remainder, skip that many days.