Question 1
Ten persons H, C, A, F, D, I, E, J, B and G are sitting around a rectangular table.
Three persons sit on each longer side, two on each shorter side, all facing the center.
H sits at the middle of a longer side. C sits at the middle of a shorter side.
A sits second to the right of H. D sits at a corner and F sits at the corner opposite to D.
Who sits second to the left of C?
Solution Approach:
Step 1: Draw rectangular table
Positions 1β10 clockwise:
- Top (longer, 3 persons): pos1(corner-TL), pos2(mid-top), pos3(corner-TR)
- Right (shorter, 2 persons): pos4(mid-right), pos5(corner-BR)
- Bottom (longer, 3 persons): pos6(mid-bot), pos7(corner-BL-ish... wait, pos7 is mid-bottom)
Correction: pos6(mid-bot), pos7(mid-bot2), pos8(corner-BL) β actually:
Bottom traversed rightβleft: pos6(mid), pos7(mid2)? For 3 persons: corner is shared with adjacent side.
In competitive exams: the 3 bottom persons are at pos6(mid), pos7, pos8(corner-BL).
Actually pos6,7,8 with pos8=BL-corner and pos5=BR-corner. β
- Left (shorter, 2 persons): pos9(mid-left), pos10(mid-left2)
- Corners: pos1(TL), pos3(TR), pos5(BR), pos8(BL)
- Longer-side midpoints: pos2(top), pos7(bottom)
- Shorter-side midpoints: pos4(right), pos9(left)
Step 2: Place persons
- H at middle of longer side β pos 7 (mid-bottom)
- C at middle of shorter side β pos 4 (mid-right)
- A second to the RIGHT of H (pos 7):
right(center-facing)=CW: pos7+2 = pos9 β A β
- D at a corner β pos 1
- F at corner OPPOSITE to D: pos5 β F β
- I second to the LEFT of C (pos 4):
left(center-facing)=anti-CW: pos4-2 = pos2 β I β
Step 3: Fill remaining positions
Remaining persons: E, J, B, G
Remaining seats: [3, 6, 8, 10]
Final Arrangement (clockwise):
pos1:D | pos2:I | pos3:E | pos4:C | pos5:F | pos6:J | pos7:H | pos8:B | pos9:A | pos10:G
Find second to the left of C (pos 4):
Left (anti-CW): pos4 β pos3 β pos2 = I
Answer: I sits second to the left of C.
Step 1: Draw rectangular table
Positions 1β10 clockwise:
- Top (longer, 3 persons): pos1(corner-TL), pos2(mid-top), pos3(corner-TR)
- Right (shorter, 2 persons): pos4(mid-right), pos5(corner-BR)
- Bottom (longer, 3 persons): pos6(mid-bot), pos7(corner-BL-ish... wait, pos7 is mid-bottom)
Correction: pos6(mid-bot), pos7(mid-bot2), pos8(corner-BL) β actually:
Bottom traversed rightβleft: pos6(mid), pos7(mid2)? For 3 persons: corner is shared with adjacent side.
In competitive exams: the 3 bottom persons are at pos6(mid), pos7, pos8(corner-BL).
Actually pos6,7,8 with pos8=BL-corner and pos5=BR-corner. β
- Left (shorter, 2 persons): pos9(mid-left), pos10(mid-left2)
- Corners: pos1(TL), pos3(TR), pos5(BR), pos8(BL)
- Longer-side midpoints: pos2(top), pos7(bottom)
- Shorter-side midpoints: pos4(right), pos9(left)
Step 2: Place persons
- H at middle of longer side β pos 7 (mid-bottom)
- C at middle of shorter side β pos 4 (mid-right)
- A second to the RIGHT of H (pos 7):
right(center-facing)=CW: pos7+2 = pos9 β A β
- D at a corner β pos 1
- F at corner OPPOSITE to D: pos5 β F β
- I second to the LEFT of C (pos 4):
left(center-facing)=anti-CW: pos4-2 = pos2 β I β
Step 3: Fill remaining positions
Remaining persons: E, J, B, G
Remaining seats: [3, 6, 8, 10]
Final Arrangement (clockwise):
pos1:D | pos2:I | pos3:E | pos4:C | pos5:F | pos6:J | pos7:H | pos8:B | pos9:A | pos10:G
Find second to the left of C (pos 4):
Left (anti-CW): pos4 β pos3 β pos2 = I
Answer: I sits second to the left of C.