Question 1
Ten persons E, J, H, G, C, F, A, I, B and D are sitting around a rectangular table.
Three persons sit on each longer side, two on each shorter side, all facing the center.
E sits at the middle of a longer side. J sits at the middle of a shorter side.
H sits second to the right of E. C sits at a corner and G sits at the corner opposite to C.
Who sits second to the left of J?
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
- E at middle of longer side β pos 7 (mid-bottom)
- J at middle of shorter side β pos 4 (mid-right)
- H second to the RIGHT of E (pos 7):
right(center-facing)=CW: pos7+2 = pos9 β H β
- C at a corner β pos 1
- G at corner OPPOSITE to C: pos5 β G β
- F second to the LEFT of J (pos 4):
left(center-facing)=anti-CW: pos4-2 = pos2 β F β
Step 3: Fill remaining positions
Remaining persons: A, I, B, D
Remaining seats: [3, 6, 8, 10]
Final Arrangement (clockwise):
pos1:C | pos2:F | pos3:A | pos4:J | pos5:G | pos6:I | pos7:E | pos8:B | pos9:H | pos10:D
Find second to the left of J (pos 4):
Left (anti-CW): pos4 β pos3 β pos2 = F
Answer: F sits second to the left of J.
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
- E at middle of longer side β pos 7 (mid-bottom)
- J at middle of shorter side β pos 4 (mid-right)
- H second to the RIGHT of E (pos 7):
right(center-facing)=CW: pos7+2 = pos9 β H β
- C at a corner β pos 1
- G at corner OPPOSITE to C: pos5 β G β
- F second to the LEFT of J (pos 4):
left(center-facing)=anti-CW: pos4-2 = pos2 β F β
Step 3: Fill remaining positions
Remaining persons: A, I, B, D
Remaining seats: [3, 6, 8, 10]
Final Arrangement (clockwise):
pos1:C | pos2:F | pos3:A | pos4:J | pos5:G | pos6:I | pos7:E | pos8:B | pos9:H | pos10:D
Find second to the left of J (pos 4):
Left (anti-CW): pos4 β pos3 β pos2 = F
Answer: F sits second to the left of J.