Circular Seating Arrangement: Basic conceptsFlame Institute

Circular Seating Arrangement: Basic concepts

Learn the essential concepts of Seating Arrangement questions along with a solved example.

What is Circular Arrangement?

In this type of arrangement, we arrange people or objects around a circle or a table. In case of people sitting around a table, the table could be of any shape i.e. rectangular, square, circular etc.

In the below arrangement, some persons are sitting around a circle and they are facing the centre. The diagram highlights the left and right of the people for this case.

Movements around the circular arrangement:

For the people facing the centre:

Left movement is called clockwise rotation.
Right movement is called anti-clockwise rotation.

For people facing outside, the opposite is true:

Left movement is called anti-clockwise rotation.
Right movement is called clockwise rotation.

The information given in such questions specifies the position of a few or all the persons in the arrangement. The positions are specified through conditions like: a particular person is sitting right or left of the other person. After reading the given information, you should draw the diagram depicting the question statement.

Positions in the circular arrangement:

Following two shapes are of six and eight people sitting around a circle.

Remember, if you are careful of the directions, then this question should be a fairly easy one to solve.

Seating Arrangement Solved Question

Given below is an example of a typical question of mixed directions (both, inside and outside).

Example: A, B, C, D, E, F, G and H are sitting around a circular area at equal distances between each other, but not necessarily in the same order. Some of the people are facing the centre while some face outside (i.e. in a direction away from the centre)

Note:

Facing the same direction means if one faces the centre then other also faces the centre and vice versa. Facing opposite direction means if one person faces the centre then the other faces outside and vice versa.

B faces outside. D sits second to the left of B. A and F are immediate neighbours of D. H sits second to the right of A. C sits third to the left of H. E sits to the immediate right of G. D sits third to the left of E. D faces the same direction as H. F sits to the immediate right of C. F and G take same directions. Find the desired arrangement.

Solution: Let us try to solve this question clue by clue:

B faces outside:

After fixing B’s position, we can see that D will be in anti-clockwise direction from B and since D is second to the left, this means there will be 1 person in between them. But we don’t know the direction of D yet, so D can be facing inside or outside.

A and F are immediate neighbours of D. H sits second to the right of A. This would give rise to 4 possibilities. First, F can be between B & D and A will be on the other side of D. Secondly, A can be between B and D while F will be on the other side of D. Each case is explained below with possible directions of ‘A’ (inside/ outside).A is sitting at other side of D (not between B and D) and F is between B and D. Now A can face inside or outside. Now in case we take A as facing outside, then 2nd to the right would be H where as we know that this position belongs to F since it is A and F who are neighbours of D, so in this situation we can take A to be facing only inside. We can also add H as 2nd anti clockwise to A and place F between B and D. Directions, of F, D and H, are not clear yet, so they could be facing inside or outside.

A could be between B and D while F could be on the other side of D. Again A could be facing outside or inside. Now in case we take A, facing inside, then 2^nd to his right would be H whereas we know that this position belongs to F since it is A and F who are neighbours of D. So in this position we can take A to be facing only outside. We can also add H at 2^nd clockwise to A and F at the other side of D. Directions, of F, D and H, are not clear yet, so they could be facing inside or outside.

C sits third to the left of H and this clue will help us choose between the above 2 possibilities. Check the 1^stdiagram in point 2, whatever direction we take H to be at, the 3^rd position, on his both sides, is already taken. So that one is rejected. We can continue the question further with the 2^nd diagram in point 4. Also we cannot take H to be facing outside, in that case moving 3 places anti-clockwise the position will clash/overlap with D. Hence H has to face inside.
E sits to the immediate right of G. D sits third to the left of E. D faces the same direction as that of H. F sits to the immediate right of C. F and G take same directions: D is 3^rdto the left of E, so one cannot take E as facing outside since in that case 3^rdleft would mean the position occupied by B. Also D will face inside since his/her and H’s direction is same. Now since F has to be on the immediate right of C, it means C will be between E and F and will face outside. Now E has to be at the immediate right of G, this means that G will be between E and H and will face outside. F will also face outside since it is given that F and G take same directions.

Circular Seating Arrangement: Key Learning