Order & ranking
Order and ranking questions — free, machine-verified practice
Order and ranking questions ask where someone stands in a line or a merit list, given positions counted from either end. The core fact is that a person's position from the left plus their position from the right always counts that person twice, so the total is left plus right minus one. Everything else in the topic is a comparison chain built from that.
Order and ranking is the highest marks-per-minute topic in the reasoning section: a question is usually one subtraction, and a prepared candidate clears a set in well under two minutes. It is also where careless candidates lose marks they had already earned, because every wrong option is built from a plausible off-by-one.
How to solve order and ranking questions in one line
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Learn the one formula that carries the topic
Total = position from left + position from right − 1. The subtraction exists because the person is counted from both sides. If A is 7th from the left and 11th from the right, the total is 7 + 11 − 1 = 17. Nearly every direct ranking question is this formula rearranged.
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Rearrange it rather than re-deriving it
If the total and one position are known, the other is total + 1 − known. Given 40 students and rank 12 from the top, the rank from the bottom is 40 + 1 − 12 = 29. Practise the rearrangement until it is automatic, because under time pressure re-deriving invites the off-by-one.
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For “how many between”, subtract and then subtract again
The number of people strictly between positions p and q is |p − q| − 1. Between the 5th and the 12th there are six people, not seven. The endpoints are not between themselves — this is the same off-by-one as the floor-puzzle gap clue, wearing different clothes.
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Build comparison clues into one chain, not a set of pairs
“A is taller than B” and “C is shorter than B” become a single ordering C < B < A. Keep extending one chain rather than holding separate facts. When a new clue cannot join the chain yet, park it and return once a bridge appears.
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Read what the chain proves, and nothing more
A chain gives order, not distance. From C < B < A you know A is tallest; you do not know whether B is closer to A or to C. Questions in this family routinely offer an option that requires exactly the extra information the chain does not carry.
The counting rules, and when each applies
The counting rules, and when each applies
| What you are asked | The rule |
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| Total, given both positions | left + right − 1 |
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| Position from the other end | total + 1 − known position |
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| People strictly between two positions | |p − q| − 1 |
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| Position after k people leave from ahead | position − k |
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| Rank in a merit list of n, given rank from bottom r | n + 1 − r |
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| Both positions given and they overlap | left + right > total + 1 ⇒ the ranges overlap |
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Practise order and ranking questions right now
Every question below was generated by the same engine that mints the Deduce daily puzzle, and machine-proven to have exactly one correct answer before it reached this page. The walkthrough is the engine's own, step for step.
Question 1
5 people are ranked in one order, from first to 5th, with no ties.
- Rohan is ranked FIRST (highest).
- Tanvi is ranked higher than Bhavna.
- Bhavna is ranked immediately below Gauri.
- Gauri is ranked immediately below Aditi.
Can you work out each person's exact position?
Show the worked solution
- Start: 120 possible rankings of 5 people.
- Clue 1 — "Rohan is ranked FIRST (highest)." ⇒ Rohan → rank 1 (top) (24 possibilities left).
- Clue 3 — "Bhavna is ranked immediately below Gauri." narrows it to 6 possibilities.
- Clue 4 — "Gauri is ranked immediately below Aditi." narrows it to 2 possibilities.
- Clue 2 — "Tanvi is ranked higher than Bhavna." ⇒ Aditi → rank 3 (3rd from top), Tanvi → rank 2 (2nd from top), Gauri → rank 4 (4th from top), Bhavna → rank 5 (bottom) (1 possibility left).
- Exactly one ranking survives every clue — that is the answer.
Question 2
5 people are ranked in one order, from first to 5th, with no ties.
- Zoya is ranked lower than Varun.
- Vikram is ranked higher than Sneha.
- Exactly 2 people are ranked between Sneha and Rahul.
- Rahul is ranked lower than Zoya.
Can you work out each person's exact position?
Show the worked solution
- Start: 120 possible rankings of 5 people.
- Clue 3 — "Exactly 2 people are ranked between Sneha and Rahul." narrows it to 24 possibilities.
- Clue 1 — "Zoya is ranked lower than Varun." narrows it to 12 possibilities.
- Clue 2 — "Vikram is ranked higher than Sneha." narrows it to 6 possibilities.
- Clue 4 — "Rahul is ranked lower than Zoya." ⇒ Vikram → rank 1 (top), Sneha → rank 2 (2nd from top), Varun → rank 3 (3rd from top), Zoya → rank 4 (4th from top), Rahul → rank 5 (bottom) (1 possibility left).
- Exactly one ranking survives every clue — that is the answer.
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Common mistakes
Forgetting the minus one
Adding position from left to position from right double-counts the person themselves. Every wrong option set in this topic contains left + right, so the answer that looks immediately available is usually the trap.
Counting the endpoints as “between”
Asked how many sit between the 4th and the 9th, the answer is four, not five or six. Write the positions out for small cases once and the rule stops needing memory.
Reading a chain as if it carried distances
An ordering tells you who is bigger, never by how much. If a question asks who is second-tallest and the chain has an unplaced person, the answer is that it cannot be determined — and “cannot be determined” is a real, frequently correct option here.
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FAQ
If A is 7th from the left and 11th from the right, how many people are in the row?
Seventeen. Position from left plus position from right counts A twice, so the total is 7 + 11 − 1 = 17. The instinctive answer of 18 is the option papers most often include, precisely because the subtraction is easy to drop under time pressure.
How do I find how many people are between two positions?
Subtract the positions and then subtract one more: |p − q| − 1. Between the 5th and the 12th there are six people, because the 5th and 12th are not between themselves. If a question says “between A and B inclusive”, drop the second subtraction and use |p − q| + 1 instead.
What does it mean when positions overlap?
If position from left plus position from right exceeds total + 1, the two counts overlap, which usually signals that two different people are being described or that the puzzle expects you to notice the range shared between them. Check the total first — a genuine contradiction is sometimes the intended answer.
Is order and ranking the same as a ranking puzzle?
They overlap. A direct ranking question is pure position arithmetic. A ranking puzzle adds an arrangement layer — several people ordered by height, age or marks with clues that must be combined before any position can be read. Deduce's Order & Ranking kind generates the puzzle form, so the practice below is the harder of the two.
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