Ranking and Order Arrangement

What does the question ask?

A group of people stand in a line, or sit in a row. You get clues about their places.

You must find a rank, a total, or the number of people between two of them.

Where do ranks come from?

A rank counts from one end of the line. Rank from the front, or from the back.

The same person has two ranks, one from each end.

Why are these questions quick to win?

Nearly all of them use one small formula.

Learn it once and you can solve most of them in seconds.

How are the two ranks linked?

Rank from the front plus rank from the back equals total plus one.

The person is counted twice, so we remove one.

Can you see why?

Take a line of 10 people. The person at the front is 1st from the front and 10th from the back.

The sum is 11, which is 10 plus 1.

Can you see it solved?

Meena is 7th from the front and 12th from the back.

Total is 7 plus 12 minus 1, which is 18 people.

Why this works: 7 people stand up to Meena and 12 stand from Meena on. Meena sits in both counts.

Can you try one more?

Dev is 15th from the front and 22nd from the back.

Total is 15 plus 22 minus 1, which is 36.

Check: 15 + 22 = 37, which is 36 + 1.

Why this works: the add-up test always gives total plus 1.

What if the total is given?

Rank from the other end equals total minus your rank, plus 1.

This is the same formula, turned around.

Can you see it solved?

A row has 30 children. Pia is 8th from the left.

Her rank from the right is 30 minus 8 plus 1, which is 23rd.

Is there a quick check?

Add the two ranks. The sum must be one more than the total.

Here 8 plus 23 is 31, which is 30 plus 1.

Why this works: 7 children stand to her left, so 30 – 7 = 23 places lie from her to the right end.

Can you try the reverse?

In a class of 45, Sana is 18th from the back.

Her rank from the front is 45 minus 18 plus 1, which is 28th.

Check: 28 + 18 = 46, which is 45 + 1.

How do you count them?

Find both positions from the same end. Subtract them, and then subtract 1.

The extra 1 removes the second person.

Can you see it solved?

Arun is 5th from the left. Bela is 14th from the left.

People between them are 14 minus 5 minus 1, which is 8.

Why this works: positions 6 to 13 sit between them, and that is 8 places.

Can you try opposite ends?

In a line of 40, Kiran is 9th from the left. Lata is 11th from the right.

Lata is 40 minus 11 plus 1, which is 30th from the left.

People between them are 30 minus 9 minus 1, which is 20.

Why this works: both ranks now count from the left, so we can subtract.

What if you must find who stands in the middle?

In a row of 25, the middle person is the 13th.

The rule is total plus 1, divided by 2. Here 26 divided by 2 is 13.

Why this works: the middle has the same rank from both ends.

What if the ranks come from opposite ends?

Turn one rank into a rank from the other end first.

Then use the same method.

What happens in a swap?

Two people trade places. A place has the same rank, but a new person now holds it.

The person who moves takes the rank of the place they move to.

How do you use this?

If a swap gives you a rank from the other end, you know the place.

Then use the main formula to find the total.

Can you see a swap solved?

Ravi is 12th from the front. Tej is 20th from the front.

They swap places. Now Ravi is 20th from the front.

Why this works: Ravi took the place Tej held, so he gets that rank.

Does the total change?

No. Nobody joins or leaves the line.

Only the people at those two places change.

What are comparison puzzles?

You get clues such as taller than, older than, or heavier than.

You must put the people in order from tallest to shortest, or the reverse.

How do you solve them?

Write each clue as a short chain with a greater-than sign. Join the chains that share a name.

Then read the finished chain from one end to the other.

Can you see it solved?

Raj is older than Sam. Sam is older than Tia. Uma is older than Raj.

The chain is Uma, Raj, Sam, Tia. So Tia is the youngest.

Why this works: each clue adds one link, and shared names let the links join.

Can you try a height puzzle?

Anil is taller than Beena. Beena is taller than Chetan. Dinesh is shorter than Chetan.

The chain is Anil, Beena, Chetan, Dinesh.

So the second tallest is Beena. The shortest is Dinesh.

Why this works: a taller-than clue only points one way, so the chain has no loops.

What mistakes cost marks?

Forgetting to subtract 1 in the main formula.

Mixing ranks from the front with ranks from the back.

How do you stay quick?

Write the formula at the top of the page. Plug in the numbers straight away.

Check the answer with the add-up test.

How should you practise?

Solve five ranking questions a day.

Then try the quiz below and read every explanation.