Concept 1 of 7
Position in a Row
Today's big idea
Left plus right minus one gives the total, since the child is counted from both ends.
Adding the two positions without subtracting counts one child twice over.
How it works
👀 What's going on?
A line of children forms at the door. You are told someone stands fourth from one end and sixth from the other, and asked how many children there are. Counting is impossible without seeing them.
💡 Here's the trick
Look at the row above. Position from the left plus position from the right does not give the total, because the child in question gets counted at both ends. Take one away and the double count disappears. So left plus right minus one is the total.
🪄 How to do it
- 1.Read off the two positions the question gives, as the row above labels them.
- 2.Add them together.
- 3.Take away one, because one child was counted from each side.
✍️ Try it
Arun is 3rd from the left and 5th from the right. How many children are in the row? Then: in a line of 11, Bela is 4th from the front, so what is her place from the back?
For the first, 3 plus 5 is 8, and taking one away gives 7 children. For the second, rearrange the same rule: 11 minus 4 plus 1 gives 8th from the back.
⚠️ Watch out
You might be thinking you simply add the two positions. Try it on the row above and you get 10 children when there are only 9. The child you are counting stands in both counts, so one of those two must go.
🌟 Why this matters
Queues, race results and seating plans all ask where somebody stands and how many there are. One small subtraction saves counting a line you cannot see.
Exam tip: Write out a row of dashes and mark the person if you are unsure; the minus one becomes obvious.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“In a row, Riya is 4th from the LEFT and 6th from the RIGHT. How many children are in the line?”
- 1
Pull the formula
Total = L + R − 1. The −1 is because Riya is counted on both sides.
- 2
Plug in
4 + 6 − 1
- 3
Compute
10 − 1 = 9.
- 4
Answer ✓
= 9 children
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Make Ravi stand 3th from the left and 2th from the right. Add children on each side.
ROW · ROUND 1 OF 3
Ravi is now 1 from left · 1 from right
Quick check
✅ VERIFICATION
In left + right - 1 = total, why do we take one away?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Odd One Out
Name what 3 share, the 4th is the odd one.