In this article, we will see how to solve slightly tougher Circular Arrangement Problems. Here,
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- different people are sitting around a circular table facing the center.
- But they all have some other peculiar characteristic which is different for everyone.
- Our job is to map everyone according to the information given.
- We then get a circular arrangement that is complex.
The particular characteristic that is different may be:
- ages
- native place
- company they work for
- favourite colour
- gender
- or any other trait
To approach this type of circular arrangement problem, you need to have patience and focus. You need to read clearly all the information provided with special focus on the words ‘left’ and ‘right’.
The 8 Steps to Follow for Circular Arrangement Problems
Table of Contents
Steps must be followed as below:
1) Read first paragraph of the problem. Note down number of persons, their gender if given & their names.
2) Read and note down the list of particular characteristics mentioned.
3) Check whether all are facing towards the center of table or outwards. Some may face inward while some outward.
4) Draw a circle with lines. Each line represents one person and indicates which direction they are facing. If all face the same direction, you can do away with the arrow heads on these lines. Then, as shown in previous article, draw left and right arrows at the bottom of the circle.
5) Now start reading the main problem. Note down all the direct information given. Start adding persons and/or their particular characteristic around circle.
6) Then go for statements which may have more than one possibility and draw possible cases.
7) Then go for statements which will give hint which possibility is true and eliminate other possibilities.
8) This way, deduce one statement at a time. You will reach the final solution. Let us explore this with an example.
Circular Arrangement Problems – Example
Representatives from eight different states viz. L, N, P, R, T, V, X and Z are sitting around a circular table facing the center but not necessarily in the same order. Each of them is from a different state namely, Maharashtra, Assam, Gujarat, Kerala, Karnataka, Delhi, Madhya Pradesh and Punjab.
V sits second to right of the representative from Kerala. Representative from Madhya Pradesh is to the immediate right of the representative from Kerala. N is third to right of the representative from Madhya Pradesh. T is to the immediate left of P. Neither P nor T is an immediate neighbor of either N or the representative from Gujarat who sits second to right of R. R is neither the representative of Kerala nor Madhya Pradesh. X and the representative from Maharashtra are immediate neighbours of each other. N is not the representative of Maharashtra. Only one person sits between P and representative from Assam. Z sits third to left of the representative from Punjab. Representative from Delhi sits second to left of the representative of Karnataka. L is not the representative of Assam.
Circular Arrangement Problems – Solution:
In this problem, 8 representatives from different states are given. So we will note them first.
Representatives: L, N, P, R, T, V, X and Z
States: Maharashtra, Assam, Gujarat, Kerala, Karnataka, Delhi, Madhya Pradesh and Punjab.
We need to map representatives to their states respectively.
Note that all are facing towards the center – so you can take your left hand as left side and right hand as right side.
Now first we will make a circle with 8 equidistant lines and left and right arrows as shown.
Now we will read the main problems and try to get the direct information. According to the problem:
1) V sits second to the right of the representative from Kerala.
2) Representative from Madhya Pradesh is to the immediate right of the representative from Kerala.
3) N is third to right of the representative from Madhya Pradesh.
Here, we will first place V at bottom most place (as shown in previous article). We then place the representative from Kerala second to the left of V. This is because V sits second to the right of representative from Kerala. Then we place the representative from Madhya Pradesh and N as given in problem. So we get the following figure.
Now no other direct information is given with which we can plot the diagram. So we move on to next statements.
4) T is to the immediate left of P.
5) Neither P nor T is an immediate neighbor of either N or the representative from Gujarat. So we get three possible cases. [Note that T is to the immediate left of P. That means we require 2 adjacent places.]
6) Representative from Gujarat sits second to right of R.
7) R is neither the representative of Kerala nor Madhya Pradesh.
So the third case gets eliminated as there is no place left for Gujarat.
Thus cases 1 and 2 get amended as shown below:
8) Only one person sits between P and the representative from Assam.
We know the possible positions of P so we can place representative from Assam accordingly.
Here for each case we get 2 cases so now we have total 4 cases.
9) Z sits third to left of the representative from Punjab.
10) Representative from Delhi sits second to left of the representative of Karnataka.
Plotting information given in these statements, possibilities 2.a and 2.b get eliminated. We can see this as below:
When we see in case 2.a and 2.b we have 4 places for these two representatives (Delhi & Karnataka).
Now, in case 2.
i) If we place the representative of Delhi as R there is no place for representative of Karnataka.
ii) If we place the representative of Delhi as N, it is possible.
iii) If we place the representative of Delhi to the left of T, there is no place for representative of Karnataka.
iv) If we place the representative of Delhi as T, there is no place for representative of Karnataka.
So placing representative of Delhi as N is possible as shown below.
The diagram looks like this.
Now we take 9^{th} statement and try to reason out 2.a again.
There are 3 possible places for Z (As representative of Madhya Pradesh, representative of Gujarat or representative of Karnataka)
i) Madhya Pradesh is not possible as there is no place for representative of Punjab.
ii) Similarly Gujarat and Karnataka are also not possible.
Thus this case 2.a is eliminated.
On similar bases, case 2.b is also getting eliminated.
Thus case 1 remains.
11) X and the representative from Maharashtra are immediate neighbours of each other.
12) N is not the representative of Maharashtra.
13) L is not the representative of Assam.
From this statement, we get that only case 1.a is valid all else gets eliminated.
Hence we get the final seating arrangement diagram of the circular arrangement as follows.
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