Logical Reasoning: Seating Arrangement
Six students-A, B, C, D, E, and F-are sitting in a row facing north. The following information is known: 1. A is sitting third to the left of D. 2. B is sitting second to the right of E. 3. C is sitting at one of the extreme ends. 4. F is sitting adjacent to D. 5. E is not sitting at any extreme end. 6. A is not adjacent to C. Determine the seating arrangement of all six students from left to right.
1. Determine the exact seating arrangement of the six students from left to right. Show your step-by-step reasoning.
Read the worked answer
Step 1: Interpret clue 1.
A is third to the left of D. This means there are two seats between A and D, with A on the left. Possible positions (1-indexed left to right): if D is at position 4, A at 1; D at 5, A at 2; D at 6, A at 3.
Step 2: Interpret clue 3.
C is at an extreme end: position 1 or 6.
Step 3: Interpret clue 5.
E is not at an extreme end, so E is at position 2, 3, 4, or 5.
Step 4: Interpret clue 2.
B is second to the right of E. So if E is at position i, B is at i+2. Thus E can be at 1,2,3,4 but not 5 or 6 (since B would be beyond 6). But E is not at extreme, so E can be at 2,3,4. Then B is at 4,5,6 respectively.
Step 5: Combine with clue 1 possibilities.
Case 1: D at 4, A at 1. Then C must be at 6 (since A at 1, C cannot be at 1 because A is there, and clue 6 says A not adjacent to C; if C at 1, adjacent to A? Actually A at 1, C at 1 impossible. So C at 6). Then E cannot be 2,3,4? Let's check: E at 2 -> B at 4, but D at 4, conflict. E at 3 -> B at 5, possible. E at 4 -> B at 6, but C at 6, conflict. So E=3, B=5. Remaining positions: 1:A, 2:?, 3:E, 4:D, 5:B, 6:C. Only F left for position 2. Check clue 4: F adjacent to D. D at 4, F at 2 is not adjacent (distance 2). So this case fails.
Case 2: D at 5, A at 2. C at 1 or 6. E at 2,3,4. But A at 2, so E cannot be 2. E at 3 -> B at 5, but D at 5 conflict. E at 4 -> B at 6. Then C cannot be 6 (B there), so C at 1. Positions: 1:C, 2:A, 3:?, 4:E, 5:D, 6:B. Remaining F at 3. Check clue 4: F adjacent to D? D at 5, F at 3 not adjacent (distance 2). Fail.
Case 3: D at 6, A at 3. C at 1 or 6. But D at 6, so C cannot be 6, thus C at 1. E at 2,3,4. E at 2 -> B at 4. E at 3 -> B at 5, but A at 3 conflict. E at 4 -> B at 6, but D at 6 conflict. So E=2, B=4. Positions: 1:C, 2:E, 3:A, 4:B, 5:?, 6:D. Remaining F at 5. Check clue 4: F adjacent to D? D at 6, F at 5 adjacent yes. Check clue 6: A not adjacent to C? A at 3, C at 1, not adjacent (distance 2) yes. All clues satisfied.
Step 6: Final arrangement.
Left to right: C, E, A, B, F, D.
Answer: The seating arrangement from left to right is C, E, A, B, F, D.
2. If the seating arrangement is reversed (i.e., all students face south instead of north), how does the arrangement change? Explain your reasoning.
Read the worked answer
Step 1: Understand the effect of facing direction.
The original arrangement was determined with all students facing north. In such arrangements, "left" and "right" are from the perspective of the students. If they face south, their left and right are reversed relative to the observer. However, the clues are given in terms of the students' perspectives. If we simply reverse the direction they face, the relative positions (who is to the left or right of whom) would be mirrored. But the problem asks: if the seating arrangement is reversed (i.e., all students face south), how does the arrangement change? Typically, if the same clues are applied with students facing south, the arrangement from left to right (observer's perspective) would be the mirror image of the north-facing arrangement. That is, the order from left to right becomes the reverse: D, F, B, A, E, C.
Step 2: Verify with an example.
In the north-facing arrangement, A is third to the left of D. If they face south, "left" for them is the observer's right. So A would be third to the observer's right of D, meaning D is to the left of A. This is consistent with the reversed order.
Step 3: Conclusion.
The arrangement from left to right (observer's perspective) would be the reverse of the north-facing arrangement: D, F, B, A, E, C.
Answer: If all students face south, the left-to-right order from the observer's perspective becomes D, F, B, A, E, C, which is the reverse of the north-facing arrangement.