This problem involves a logical deduction based on seating arrangement clues. We need to determine the exact positions of seven people (A, B, C, D, E, F, G) sitting in a row facing north and then count how many people are to the right of person F.
Deducing Seating Arrangement Step-by-Step
Let's break down the clues to determine the order:
1. Identifying the Rightmost Position
Clue: "No one sits to the right of B."
Since everyone is facing north, the person on the extreme right has no one to their right. This means B must be in the last position.
- Total people: 7
- Position of B: $7^{th}$
Current Arrangement: $_ _ _ _ _ _ B$
2. Placing Person A Relative to B
Clue: "Only two people sit between B and A."
With B in the $7^{th}$ position, there are two spots between B and A. This places A three positions to the left of B.
- Calculation: Position of A = Position of B - 2 - 1 = $7 - 2 - 1 = 4$
- Position of A: $4^{th}$
Current Arrangement: $_ _ _ A _ _ B$
3. Placing Person D Relative to A
Clue: "A sits to the immediate left of D."
Since A is in the $4^{th}$ position, D must be immediately to A's right.
- Position of D: $5^{th}$
Current Arrangement: $_ _ _ A D _ B$
4. Placing Person E Relative to D
Clue: "Only three people sit between E and D."
D is in the $5^{th}$ position. Counting three people between E and D means E must be three positions to the left of D, plus the space for D itself. Thus, E is $5 - 3 - 1 = 1^{st}$ position.
- Position of E: $1^{st}$
Current Arrangement: $E _ _ A D _ B$
5. Placing the F-G Pair
Clue: "G sits to the immediate right of F."
This means F and G sit together in the order 'FG'.
Looking at the current arrangement $E _ _ A D _ B$, the available positions are $2^{nd}$, $3^{rd}$, and $6^{th}$. The 'FG' pair needs two adjacent spots. The only available adjacent spots are the $2^{nd}$ and $3^{rd}$ positions.
- Position of F: $2^{nd}$
- Position of G: $3^{rd}$
Current Arrangement: $E F G A D _ B$
6. Placing the Final Person
The only person left to place is C, and the only position left is the $6^{th}$ position.
- Position of C: $6^{th}$
7. Final Arrangement
Combining all the placements, the final seating arrangement from left ($1^{st}$) to right ($7^{th}$) is:
| Position | $1^{st}$ | $2^{nd}$ | $3^{rd}$ | $4^{th}$ | $5^{th}$ | $6^{th}$ | $7^{th}$ |
| Person | E | F | G | A | D | C | B |
8. Answering the Question
Question: How many people sit to the right of F?
Person F is in the $2^{nd}$ position.
The people sitting to the right of F (positions $3^{rd}$ to $7^{th}$) are G, A, D, C, and B.
Counting these individuals:
- G ($3^{rd}$)
- A ($4^{th}$)
- D ($5^{th}$)
- C ($6^{th}$)
- B ($7^{th}$)
There are 5 people sitting to the right of F.
Important Questions from Seating Arrangement (Notes)
- Five friends are sitting on a bench in the following order :
(i) P is sitting next to Q and R is next to S.
(ii) S is not sitting with T; T is on the extreme left hand side of the bench and R is on second position from the right hand side.
(iii) P is on the right hand side of Q and to the right side of T. (iv) P and R sitting together
Who is sitting exactly in the middle ? Seven people, C, D, E, F, L, M and N, are sitting in a row, facing north.
Only two people sit to the right of C. Only two people sit between C and L. Only two people sit between E and N. N sits to the immediate left of C. M sits to the immediate right of F. Who sits at the third position from the left end of the row?Seven boxes, A, B, C, D, E, F and G, are kept one over the other but not necessarily in the same order. Only A is kept above F. Only D is kept between F and C. Only E is kept below B. How many boxes are kept below C?
P, Q, R, S, T, U and V are sitting in a row, facing north. No one sits to the left of U. Only four people sit between U and R. Only three people sit to the right of V. P sits to the immediate left of S. Q is not an immediate neighbour of V. How many people sit between P and T?
A, B, C, D, J, K and L are sitting around a circular table facing the centre of the table. K sits to the immediate right of B. Only three people sit between K and A when counted from the left of K. Only three people sit between B and L. C sits to the immediate right of D. How many people sit between J and D when counted from the left of D?
