Arranging Friends in a Line: Step-by-Step Solution
This problem involves arranging six friends (D, E, F, G, J, K) in a straight line facing north based on several conditions. We need to find the number of people sitting between E and D.
1. Determine the Total Positions
There are six friends, so there are 6 positions in the line. Since they face north, position 1 is the leftmost and position 6 is the rightmost.
2. Place Key Individuals Based on Clues
- Clue: "No one sits to the right of K."
This means K must be in the rightmost position. Position: _ _ _ _ _ K (6)
- Clue: "Only one person sits between F and K."
With K at position 6, the only possibility is that F is at position 4, leaving position 5 empty between them. Positions: _ _ _ F _ K (4, 5, 6)
- Clue: "Only three people sit between K and J."
K is at position 6. Three people between them means J must be at position 2. The positions between K and J are 5, 4, and 3. Positions: _ J _ _ _ K (2, ?, ?, ?, 6) Combined arrangement so far: Positions: _ J _ F _ K (1, 2, 3, 4, 5, 6)
3. Place Remaining Friends
The remaining friends are E, G, and D. The remaining positions are 1, 3, and 5.
- Clue: "G sits at some place to the left of D but at some place to the right of E."
This establishes the relative order: E ... G ... D.
- Assigning Positions:
- To satisfy E ... G ... D using positions 1, 3, and 5, E must be at position 1.
- G must be at position 3.
- D must be at position 5.
4. Final Seating Arrangement
The complete arrangement from left (1) to right (6) is:
E J G F D K
Positions: 1 2 3 4 5 6
5. Calculate People Between E and D
E is at position 1 and D is at position 5.
The people sitting between E and D are those at positions 2, 3, and 4.
These individuals are J, G, and F.
Therefore, there are 3 people sitting between E and D.
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Select the correct answer using the code given below:
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