Circular Seating Arrangement Puzzle

Mental Calculation, Mathematics, and Puzzles
1

Eight persons I, J, K, L, M, N, O and P are sitting around a circular table but not necessarily in the same order. Five of them are facing inward while other are facing outwards.
M is third to the right of K. N sits third to the left of M. Three persons sit between N and J. O sit third to the right of N who is not facing the centre. L sits third to the right of I, who is not facing the centre.

Who sits exactly between N and I?
(a) J
(b) K
(c) M
(d) L
(e) None of these

How would you solve it ?

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3

This is the answer
I solved it finally

Click here to view the answer

IMG_20220630_084709
IMG_20220630_0847091920×1920 66.6 KB

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Click here to view the answer

16565591341204896326144084352652
165655913412048963261440843526521920×2560 183 KB

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Yeah I solved it…I didn’t have the answer. It was a practice question without solution. I am also trying to solve after giving questions

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See I solved it like a linear arrangement. Both have same answer. I mean there is P exactly in between N and I. No necessary to draw a circle or no need to solve it like a circle

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I know method on how to decide its direction actually. K is placed at a position that must decides its direction :slight_smile:

M is third to the right of K.

See if I would chose K’s direction to inside then I cant place M. As M is placed first I force K in such a way that M is third to the right.

N’s direction outside

M is third to the left of M

I have to place M first

— — — — — — — —

Then
— — — — N(1)— — M( )

1 is out and 0 is in

O sits third to the right of N who doesn’t face centre

— O( ) — — N(1) — — M( )

M is third to the right of K

That means

K is third left of M

Can I place K in place of N

So I will place K like this and K faces only outside.
— O( ) K(1) — N(1) — — M( )

Now K is facing outward and noted that down as K(1)

Since I can’t understand directions in circle so I am using this method like breaking the circle into a line.

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Despite my best efforts, I haven’t been able to crack the puzzle just yet.

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I did use a circle!
N seemed key, reading through it says they are facing outward.

J is directly opposite as 3 spaces either side of N, it doesn’t matter if you go clockwise or not.

O was next, which then allowed M (N is 3rd left of it and O had already taken the other possible slot).

With M, K can be worked out. From this, the outward letters are N (given), I (given), K (deduced).

I and L next, to fit the constraint cited.

P is last and turns out to be the one between N & I.

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14

Funny, I would have gone with 1n and 0ut !

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My solution
  1. Assume K’s right side direction is: —>
    K _ _ _ _ _ _ _
  2. M is third to the right of K
    K _ _ M _ _ _ _
  3. N sits third to the left of M
    K and M must sit in opposite directions, otherwise N would be in place of K
    K _ _ M _ _ N _
  4. Three persons sit between N and J
    From both sides there are 3 people between N and J, because total count is 8.
    N + 3 + J + 3 = 8, so only one spot for J
    K _ J M _ _ N _
  5. O sit third to the right of N who is not facing the centre
    There are 2 possible places on left and right, one is occupied by M, so it must be the place next to K. Also because of this, K is not facing the center too, K and N has same sense of direction so far
    K O J M _ _ N _
  6. L sits third to the right of I, who is not facing the centre
    Between I and L should sit two people, so there are two solutions:
    K O J M L _ N I WRONG
    K O J M I _ N L CORRECT
    because it was said ‘I’ is not facing center, same sense of direction as K and N
    K O J M I _ N L
  7. Who sits exactly between N and I?
    Only the person P is left, who is conveniently between N and ‘I’
    K O J M I P N L

ANSWER: P and K, N, I are not facing center of circle.