Seating arrangement

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Seating arrangement — Logical Reasoning Questions & Formulas

Logical Reasoning

6 questions

Linear (in a row)

$n$ people in a row: $n!$
$n$ people in $r$ seats: ${}^{n}P_{r} = \dfrac{n!}{(n-r)!}$
A block of $r$ people together: $(n - r + 1)! \times r!$
Two people never together: $n! - (n-1)!\times 2!$
$m$ men and $n$ women alternately ( $m = n$ ): $2 \times m! \times n!$

Circular (around a table)

$n$ people: $(n-1)!$
A block of $r$ together: $(n - r)! \times r!$
$m$ men, $n$ women alternately ( $m = n$ ): $(m-1)! \times n!$
Beads on a necklace (clockwise = anticlockwise): $\dfrac{(n-1)!}{2}$

For arrangement puzzles (not counting), draw the row or circle, place the most-constrained clue first, and pencil in only definite positions before guessing.

1.
A, B, C, D, and E are friends sitting in a row facing north. A is sitting at one of the ends. B is sitting to the right of C. D is sitting between B and E. C is not sitting at any of the ends. Who is sitting exactly in the middle?
Choose an answer
2.
Six people A, B, C, D, E, and F are sitting around a circular table facing the centre. A is to the immediate left of B. C is between D and E. F is to the immediate right of E. Who is to the immediate left of D?
Choose an answer
3.
Ten people are sitting in two parallel rows containing five people each. Row 1 consists of Q, R, S, T, and P facing south. Row 2 consists of A, B, C, D, and E facing north. R sits exactly in the middle of the row. A sits second to the left of the person who faces R. Only one person sits between A and B. Q sits second to the right of the person who faces B. P sits at an extreme end and faces D. C sits to the immediate left of D. S is not adjacent to P. Who faces S?
Choose an answer
4.
Eight friends P, Q, R, S, T, U, V, and W are sitting around a square table. Four sit at the corners facing the center, and four sit in the middle of the sides facing outside. P, who faces the center, sits third to the right of V. T, who faces the center, is not an immediate neighbor of V. Only one person sits between V and W. S sits second to the right of Q. Q faces the center. R is not an immediate neighbor of P. Who sits second to the left of R?
Choose an answer
5.
Seven people A, B, C, D, E, F, and G are sitting in a straight line facing north. Each of them has a different profession: Doctor, Engineer, Teacher, Pilot, Lawyer, Manager, and Architect. D sits third to the right of the Teacher. The Lawyer sits second to the left of D. Only one person sits between the Lawyer and the Architect. A sits immediate right of the Architect. C is a Manager and sits at one of the extreme ends. B sits third to the left of F, who is a Pilot. E does not sit adjacent to D. The Doctor sits to the immediate left of the Engineer. What is the profession of A?
Choose an answer
6.
Eight persons J, K, L, M, N, O, P, and Q are sitting around a circular table facing the center. L sits third to the right of K. N sits second to the left of L. P sits to the immediate right of N. Q sits second to the right of P. M sits to the immediate right of Q. O is not an immediate neighbor of K. Who sits opposite to M?
Choose an answer

0/6 answered

Logical Reasoning

Seating arrangement

6 questions

Linear (in a row)

$n$ people in a row: $n!$
$n$ people in $r$ seats: ${}^{n}P_{r} = \dfrac{n!}{(n-r)!}$
A block of $r$ people together: $(n - r + 1)! \times r!$
Two people never together: $n! - (n-1)!\times 2!$
$m$ men and $n$ women alternately ( $m = n$ ): $2 \times m! \times n!$

Circular (around a table)

$n$ people: $(n-1)!$
A block of $r$ together: $(n - r)! \times r!$
$m$ men, $n$ women alternately ( $m = n$ ): $(m-1)! \times n!$
Beads on a necklace (clockwise = anticlockwise): $\dfrac{(n-1)!}{2}$

For arrangement puzzles (not counting), draw the row or circle, place the most-constrained clue first, and pencil in only definite positions before guessing.

1.
A, B, C, D, and E are friends sitting in a row facing north. A is sitting at one of the ends. B is sitting to the right of C. D is sitting between B and E. C is not sitting at any of the ends. Who is sitting exactly in the middle?
Choose an answer
2.
Six people A, B, C, D, E, and F are sitting around a circular table facing the centre. A is to the immediate left of B. C is between D and E. F is to the immediate right of E. Who is to the immediate left of D?
Choose an answer
3.
Ten people are sitting in two parallel rows containing five people each. Row 1 consists of Q, R, S, T, and P facing south. Row 2 consists of A, B, C, D, and E facing north. R sits exactly in the middle of the row. A sits second to the left of the person who faces R. Only one person sits between A and B. Q sits second to the right of the person who faces B. P sits at an extreme end and faces D. C sits to the immediate left of D. S is not adjacent to P. Who faces S?
Choose an answer
4.
Eight friends P, Q, R, S, T, U, V, and W are sitting around a square table. Four sit at the corners facing the center, and four sit in the middle of the sides facing outside. P, who faces the center, sits third to the right of V. T, who faces the center, is not an immediate neighbor of V. Only one person sits between V and W. S sits second to the right of Q. Q faces the center. R is not an immediate neighbor of P. Who sits second to the left of R?
Choose an answer
5.
Seven people A, B, C, D, E, F, and G are sitting in a straight line facing north. Each of them has a different profession: Doctor, Engineer, Teacher, Pilot, Lawyer, Manager, and Architect. D sits third to the right of the Teacher. The Lawyer sits second to the left of D. Only one person sits between the Lawyer and the Architect. A sits immediate right of the Architect. C is a Manager and sits at one of the extreme ends. B sits third to the left of F, who is a Pilot. E does not sit adjacent to D. The Doctor sits to the immediate left of the Engineer. What is the profession of A?
Choose an answer
6.
Eight persons J, K, L, M, N, O, P, and Q are sitting around a circular table facing the center. L sits third to the right of K. N sits second to the left of L. P sits to the immediate right of N. Q sits second to the right of P. M sits to the immediate right of Q. O is not an immediate neighbor of K. Who sits opposite to M?
Choose an answer

0/6 answered