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Concept 5 of 8

Position in a Row: From the Left, From the Right

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Today's big idea

Left position plus right position always makes one more than the total.

3rd from the left and 4th from the right adds to 7, in a row of 6.

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How it works

👀 What's going on?

Five children line up for assembly. Ravi is 2nd from the left. Ask where he stands from the other end and the same child suddenly has a different number. Both are right, because a position means nothing until you say which end you counted from.

💡 Here's the trick

From-left + From-right = Total + 112345678910← from leftfrom right →3rd from left4th from rightBetween = (later) − (earlier) − 1Here: 7 − 3 − 1 = 3 children between

Look at the row above. That same child is 3rd from the left and 4th from the right, and 3 + 4 makes 7 in a row of only 6. The extra one is the child themselves, counted once from each end. So position from the left plus position from the right always equals the total plus 1.

🪄 How to do it

  1. 1.Write down what you know, as the picture above gives both of that child's positions.
  2. 2.Use the link: left position plus right position equals the total plus 1.
  3. 3.Rearrange that link for whichever piece is missing.

✍️ Try it

In a row of 9, Meera is 4th from the left, so where is she from the right? Then, if Sam is 5th from the left and 6th from the right, how long is the row?

Meera is 9 − 4 + 1 = 6th from the right, and checking, 4 + 6 = 10, one more than 9. Sam's row holds 5 + 6 − 1 = 10 children. The same link solved both, simply rearranged.

⚠️ Watch out

You might be thinking left position plus right position gives you the total. It gives one more than the total, because the child gets counted from both ends. Forgetting that leaves you off by one every single time.

🌟 Why this matters

Finding your row in a cinema, or working out where you stand in a queue, both run on this. Drawing the row settles any doubt in seconds.
Exam tip: Check your answer against the link, because the two positions have to add to one more than the total.

3

Watch me solve one

Quanta solves it

“Watch how I think through one of these — then you try.”

THE PROBLEM

“Ravi is 6th from the left and 3rd from the right. How many children are in the line?”

  1. 1

    Add both positions

    6 + 3 = 9

  2. 2

    Ravi got counted twice

    He is counted once from each end, so take one away.

  3. 3

    Answer ✓

    = 8 children

Now you try one — same steps, different story 👇

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See it in action

⚡ Time to play!

Make Ravi stand 2th from the left and 4th from the right. Tap to add children on each side.

POSITION · ROUND 1 OF 3

L
🧒
R

Ravi is now 1 from left · 1 from right

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Quick check

✅ VERIFICATION

In a row of 12 children, Anu is 5th from the left. What is her position from the right?

⚡ Finish the activity above first to answer.

Keep going!

Up next: Who Has What

Every tick clears its row AND its column. Then look for a lone box.

Concept 6 of 8 →