Ranking and Order made clear.
Draw the two ends of the row and mark the person being ranked. Most ranking formulas simply count the people on each side without counting that person twice.
Key concepts in Ranking and Order
One person, two ends
Total N = rank from left + rank from right − 1, assuming unique positions and no ties.
Opposite rank
Right rank = N−left rank+1.
Between two positions
If positions p and q are measured from the same end, the number strictly between them is |p−q|−1.
Swapping positions
After two people exchange places, each takes the other’s old position; convert all ranks to one end first.
Two-ended ranking
| Left side | Person | Right side | Total |
|---|---|---|---|
| 6 people | Ravi: 7th from left | 8 people | 6+1+8 = 15 |
| Rank from left: 7 | Counted in both ranks | Rank from right: 9 | 7+9−1 = 15 |
A reliable solving method
- Label the end used by each rank.
- Convert opposite-end ranks into the same coordinate system.
- Count endpoints carefully: “between” excludes both people.
- Check whether the clues specify which person is ahead.
Step-by-step solved examples
Ravi is 7th from left and 9th from right. Total people?
- Six people stand to Ravi’s left and eight to his right.
- Include Ravi once: 6+1+8.
- Total = 15.
In a row of 30, Ana is 12th from left. Rank from right?
- There are 30−12 = 18 people after Ana.
- Counting Ana as the first from that side gives 18+1.
- Rank from right = 19.
A is 4th and B 11th from the left. How many between?
- The positions strictly inside are 5 through 10.
- Compute 11−4−1.
- There are 6 people between them.
Ranking and Order: practice questions
Choose one answer before opening the explanation. Write down your reasoning as well as the option; a correct guess is different from a method you can repeat.
5th from left and 8th from right: total?
Show answer and explanation — question 1
Answer B: 12
5+8−1 = 12.
In 20 people, 6th from left is what from right?
Show answer and explanation — question 2
Answer B: 15th
20−6+1 = 15.
People between positions 3 and 9?
Show answer and explanation — question 3
Answer B: 5
9−3−1 = 5.
In 25 people, last from left is what from right?
Show answer and explanation — question 4
Answer A: 1st
The far-right endpoint is first from the right.
A at 4, B at 10 from left swap. A’s new left rank?
Show answer and explanation — question 5
Answer C: 10
A takes B’s old position 10.
With no ties, 10th highest among 40 is what from lowest?
Show answer and explanation — question 6
Answer C: 31st
40−10+1 = 31.
Frequently asked questions
Why subtract one in the total formula?
The same person appears in both rank counts, so one duplicate is removed.
Can I use the formula for competition ranks with ties?
Not without further information about tie handling; the simple rule assumes distinct positions.
Label the end used by each rank. Check whether the clues specify which person is ahead.