Position Puzzles

In this type of questions, the rank/position of a person(s) from either of the two ends of a row/queue is given and we have to determine:

• Either the total number of persons in the group
• Or the number of persons to the left/right of a particular person.
• Or the number of persons between two given persons.

Sometimes, such questions are given in the form of a puzzle involving interchanging of seats by two or more persons.

Types of Position Puzzles

Finding position from other end

Q. In class of 45 students rank of Mragank is 15th from the top, then rank of Mragank from the bottom is

(a) 30         (b) 31          (c) 32          (d) 33

Explanation:

Mragank’s rank from the bottom = (Total number of students + 1) — Rank of Mragank from top
= (45 + 1) - 15 = 46 – 15 = 31

Answer: (b)

Finding the number of persons between two given persons

Let’s see a couple of questions wherein the number of people between two given individuals is to be found out. Do read and compare the following two questions.

Q. In class of 45 students rank of Mragank is 15th from the top, and that of Aanya is 22nd from the top. How many students must be there between the two?

(a) 5         (b) 6          (c) 8          (d) Cannot be determined

Explanation:

We have been given the position of Mragank and Aanya from the same side (i.e. from the top). So, our task is easy.

(If their positions had been given from different sides, then we would first have found out their positions from one side.)

Note that the data, that there were 45 students in the class, is not required/used. It’s because we already know the positions of both the individuals from the same side. If we would have been given their positions from separate ends, then we would have used this data.

Number of students between Mragank and Aanya = (22 - 15) - 1 = 7 - 1 = 6

Alternate Method:

Number of students between Mragank and Aanya = 21 - 15 = 6

If we do 22 - 15 = 7, then this will also include Aanya. It will be wrong, as we have to find the number of students between Mragank and Aanya, excluding both Mragank and Aanya.

Answer: (b)

Q. In class of 45 students rank of Mragank is 15th from the top, and that of Aanya is 22nd from the bottom. How many students must be there between the two?

(a) 5         (b) 6          (c) 8          (d) Cannot be determined

Explanation:

Their positions had been given from different sides. So, we would first find out their positions from one side (either their ranks from the top, or their ranks from the bottom).

Note that the data, that there were 45 students in the class, will be required/used here. It’s because we have been given their positions from separate ends. If we would have already known their positions from the same side, then we would not have used this data.

Rank of Mragank = 15th from the top.

Rank of Aanya = 22nd from the bottom

So, Rank of Aanya from the top = (Total number of students + 1) — Rank from the bottom = (45 + 1) - 22 = 24

Number of students between Mragank and Aanya = (24 - 15) - 1 = 9 - 1 = 8

Alternate Method:

Number of students between Mragank and Aanya = 23 - 15 = 8

If we do 24 - 15 = 9, then this will also include Aanya. It will be wrong, as we have to find the number of students between Mragank and Aanya, excluding both Mragank and Aanya.

Answer: (c)

Finding the total number of persons in the row

Now, let’s see a question wherein total number of people in the row are to be found out.

In such questions, our goal should be to find the position of a certain individual from both ends.

Q. In a class of students, Mragank is 25th from top and 32nd from bottom in a class, then total number of students in the class is

(a) 55         (b) 57          (c) 56          (d) 58

Explanation:

Here, the position of Mragank from both ends is already given. So, our task is easy.

Total students in a class = (Rank of Mragank from top + Rank of Mragank from bottom) — 1
= (25 + 32) — 1
= 57 — 1 = 56

Alternate Method:

Mragank is 25th from top and 32nd from bottom.

Total students in a class = (Total number of students before Mragank + Total number of students after Mragank) + 1
= 24 + 31 + 1
= 55 + 1 = 56

Answer: (c)

Questions where people change their positions

Now, once we have understood the basics, let’s see some questions wherein people change their positions.

Q. In a row of 40 girls, when Alka was shifted to her left by 4 places, her place from the left end of the row became 10. What is the position of Aanya from the right end of the row, if Aanya was three places to the right of Alka’s original position?

(a) 24         (b) 23          (c) 22          (d) 25

Explanation:

On shifting 4 places to the left, Alka’s position = 10th from the left end.

Thus, Alka’s original position = 10 + 4 = 14th from the left end.

Aanya is 3 places to the right of Alka’s original position = 17th from the left end.

Now, Aanya’s position from right = (Total number of girls + 1) — Aanya’s position from left = (40 + 1) — 17 = 41 - 17 = $24^{th}$

Answer: (a)

Questions with multiple cases

In such questions, multiple cases may arise (generally two cases). We have to keep both cases in mind while answering the questions.

Q. If in a row, Rohan is 10th from left and Mukesh is 13th from right and there are four persons in between Rohan and Mukesh, then find the maximum and minimum number of persons in the row.

(a) 27, 18         (b) 30, 15          (c) 27, 17          (d) 30, 19

Explanation:

Two cases may arise in this question, depending on the relative position of Rohan and Mukesh.

Case I: For maximum number of persons

Total number of persons = Sum of positions of both persons + Number of persons in middle
= 10 + 13 + 4 = 27

Case II: For minimum number of persons

Total number of persons = Sum of positions of both places — Number of persons in middle including Mukesh and Rohan who have been counted twice
= (10 + 13) — (4 + 2) = 23 – 6 = 17

Answer: (c)