Five boxes B1, B2, B3, B4 and B5 are placed one above the other in racks. The…
2021
Five boxes B1, B2, B3, B4 and B5 are placed one above the other in racks. The lowermost rack is numbered as one, the rack just above it as two, and so on up to five. Each box is coloured with a different colour out of L1, L2, L3, L4 and L5 (not necessarily in the same order). Some clues are given:
Box B4 is placed in the topmost rack.
Two boxes are placed between the L2 coloured box and the L5 coloured box.
The L1 coloured box is placed immediately above the L5 coloured box.
The L5 coloured box is placed above the L4 coloured box.
Box B3 is coloured with L4.
Box B2 is coloured with L1.
Box B1 is not placed immediately above box B3.
Which of the following boxes are placed immediately above and immediately below box B5, respectively?
Answer: D. B2 and B3 — Concept: A vertical 'stacking' arrangement is solved by converting every clue into an absolute rack number (1 = bottom, 5 = top). Anchor the fixed clue first,…
- A.
B3 and B2
- B.
B4 and B1
- C.
B1 and B3
- D.
B2 and B3
Attempted by 23 students.
Show answer & explanation
Correct answer: D
Concept: A vertical 'stacking' arrangement is solved by converting every clue into an absolute rack number (1 = bottom, 5 = top). Anchor the fixed clue first, then place colours/positions whose gaps and 'immediately above/below' relations are forced, and finally read off the neighbours of the asked element.
Application — fix positions step by step:
B4 is in the topmost rack, so B4 is at rack 5.
'Two boxes between L2 and L5' means their racks differ by 3, so the pair is {rack 1, rack 4} or {rack 2, rack 5}. 'L1 immediately above L5' needs a rack directly above L5, and 'L5 above L4' needs at least one rack below L5, so L5 cannot be at rack 1 or rack 5.
Test L5 at rack 4: then L2 is at rack 1 and L1 (immediately above L5) is at rack 5. But L1 is box B2, and rack 5 is already taken by B4 — a contradiction. So L5 is not at rack 4.
Therefore L5 is at rack 2 and L2 at rack 5; L1 (immediately above L5) is at rack 3. Since L5 is above L4, L4 must be at rack 1; the remaining colour L3 takes rack 4. Colour order bottom-to-top is L4, L5, L1, L3, L2.
Map boxes to colours: B2 = L1 -> rack 3; B3 = L4 -> rack 1; B4 = L2 -> rack 5 (consistent). The two boxes left, B1 and B5, take racks 4 and 2 (colours L3 and L5).
'B1 is not immediately above B3': B3 is at rack 1, so B1 cannot be at rack 2. Hence B1 is at rack 4 and B5 is at rack 2.
Final stack, top to bottom: rack 5 = B4 (L2), rack 4 = B1 (L3), rack 3 = B2 (L1), rack 2 = B5 (L5), rack 1 = B3 (L4).
Cross-check: B5 sits at rack 2, so the box immediately above it (rack 3) is B2 and the box immediately below it (rack 1) is B3. Every clue holds, so the box above B5 is B2 and the box below B5 is B3.