Question 1

Four boxes W, X, Y, and Z are stacked in a tower. Box Y is not at the top. Box W is directly above Box X. Box Z is at the bottom. Which box is at the top?

Accepted Answer

Position 1 (bottom): Z (given). Position 4 (top): must be determined. W is directly above X, so they occupy consecutive positions. Y is not at the top. Possible arrangements: Z at 1, then positions 2, 3, 4 for W, X, Y. Since W is directly above X: either X at 2 and W at 3, or X at 3 and W at 4. If X at 3 and W at 4, then Y at 2. This satisfies Y not at top. If X at 2 and W at 3, then Y at 4, but Y cannot be at top. Therefore: Z at 1, Y at 2, X at 3, W at 4. W is at the top.

Question 2

Five boxes labeled A, B, C, D, and E are stacked vertically on top of each other. Box C is placed directly above Box A. Box E is at the bottom. Box B is directly above Box E. Box D is at the top. Which box is in the middle (3rd position)?

Accepted Answer

This is a straightforward linear stacking puzzle. We need to arrange 5 boxes in order from bottom to top using the given constraints: E is at bottom (position 1), B is directly above E (position 2), C is directly above A (consecutive positions), D is at top (position 5). Since D is at top and B at position 2, C and A must occupy positions 3 and 4. Since C is directly above A, A is at position 3 and C at position 4. Therefore position 3 (middle) = A.

Question 3

Six boxes are stacked in a tower. Box P is 2 positions above Box M. Box N is at the 4th position. Box L is at the bottom. Box Q is directly above Box L. Box R is at the top. What is the position of Box P?

Accepted Answer

We have 6 positions. L is at position 1 (bottom). Q is directly above L, so Q is at position 2. R is at position 6 (top). N is at position 4 (given). P is 2 positions above M, meaning if M is at position X, then P is at position X+2. Remaining positions to fill: 3 and 5 for boxes M and P. If M is at position 3, then P is at position 5. This satisfies all constraints. Therefore P is at position 5.

Question 4

Five boxes labeled 1, 2, 3, 4, and 5 are stacked vertically. Box 3 is exactly in the middle. Box 1 is directly above Box 2. Box 5 is at the bottom. Which box is at the top?

Accepted Answer

With 5 boxes, the middle position is position 3. Box 3 is at position 3 (middle). Box 5 is at position 1 (bottom). Box 1 is directly above Box 2, so they are consecutive. Remaining boxes: 1, 2, 4 for positions 2, 4, 5. Box 1 directly above Box 2: either (Box 2 at 2, Box 1 at 3) or (Box 2 at 4, Box 1 at 5). Since Box 3 is at position 3, Box 1 cannot be at position 3. So Box 2 at 4, Box 1 at 5. Then Box 4 at position 2. Arrangement: Position 1=Box 5, Position 2=Box 4, Position 3=Box 3, Position 4=Box 2, Position 5=Box 1. Box 1 is at the top.

Question 5

Five boxes labeled A, B, C, D, and E are stacked vertically in positions 1 to 5 (1 = bottom, 5 = top). The following conditions apply:
(i) Box C is exactly 2 positions above Box A.
(ii) Box B is immediately above Box D.
(iii) Box E is not at the top.
(iv) Box A is not at the bottom.

Which box is at position 3?

Accepted Answer

This is a constraint satisfaction puzzle requiring systematic elimination. From condition (i), C is 2 above A, giving pairs: (A=1,C=3), (A=2,C=4), or (A=3,C=5). Condition (iv) eliminates A=1. Condition (ii) requires B immediately above D. Testing (A=2,C=4): B and D must be consecutive. Remaining positions are 1,3,5. If D=1,B=2, then E=5, violating condition (iii). If D=3,B=4, then C=4 conflicts. If D=5, B cannot be above. Testing (A=3,C=5): Remaining positions 1,2,4 for B,D,E. If D=1,B=2, then E=4. This satisfies all conditions: D=1, B=2, A=3, E=4, C=5.

Question 6

Eight boxes are stacked vertically in positions 1 (bottom) to 8 (top). The boxes are labeled A, B, C, D, E, F, G, H. The following conditions apply:
(i) Box C is 3 positions above Box A.
(ii) Box E is immediately below Box B.
(iii) Box D is at position 2.
(iv) Box G is above Box E but below Box C.
(v) Box H is not at position 8.

Which box is at position 5?

Accepted Answer

From condition (iii), Box D is at position 2. From condition (i), Box C is 3 positions above Box A. Possible pairs: (A=1,C=4), (A=2,C=5), (A=3,C=6), (A=4,C=7), (A=5,C=8). Since D=2, (A=2,C=5) is invalid. From condition (ii), Box E is immediately below Box B, so B = E + 1. From condition (iv), G is above E and below C. From condition (v), H is not at position 8. Testing (A=1,C=4): Remaining positions {3,5,6,7,8} for {B,C,E,F,G,H}. C=4, so remaining {3,5,6,7,8} for {B,E,F,G,H}. From (ii), E and B consecutive. From (iv), E < G < C=4, so G ∈ {3} (since E < G and G < 4). If G=3, then E ∈ {1,2} (but A=1, D=2). No valid E. Testing (A=3,C=6): Remaining positions {1,4,5,7,8} for {B,C,E,F,G,H}. C=6, so remaining {1,4,5,7,8} for {B,E,F,G,H}. From (iv), E < G < 6. From (ii), B = E+1. If E=1, B=2 (but D=2). If E=4, B=5, G ∈ {5} (but B=5). If E=5, B=6 (but C=6). No valid solution. Testing (A=4,C=7): Remaining positions {1,3,5,6,8} for {B,C,E,F,G,H}. C=7, so remaining {1,3,5,6,8} for {B,E,F,G,H}. From (iv), E < G < 7. From (ii), B = E+1. If E=1, B=2 (but D=2). If E=3, B=4 (but A=4). If E=5, B=6, G ∈ {6} (but B=6). If E=6, B=7 (but C=7). No valid solution. Testing (A=5,C=8): Remaining positions {1,3,4,6,7} for {B,C,E,F,G,H}. C=8, so remaining {1,3,4,6,7} for {B,E,F,G,H}. From (iv), E < G < 8. From (ii), B = E+1. If E=1, B=2 (but D=2). If E=3, B=4, G ∈ {4,5,6,7} (but A=5, B=4). G ∈ {6,7}. If G=6, remaining {1,7} for {F,H}. H not at 8 ✓. Valid: H at 1 or 7, F at 7 or 1. If G=7, remaining {1,6} for {F,H}. H not at 8 ✓. Valid. If E=4, B=5 (but A=5). If E=6, B=7, G ∈ {7} (but B=7). If E=7, B=8 (but C=8). So E=3, B=4, G ∈ {6,7}. Remaining positions {1,6,7} for {F,G,H}. If G=6, then {F,H} at {1,7}. If G=7, then {F,H} at {1,6}. Both are valid. The puzzle has multiple solutions. However, if we assume the most straightforward assignment: E=3, B=4, G=6, then {F,H} at {1,7}. Position 5 = A. But A is at position 5 in the setup (A=5 means Box A is at position 5). So the answer is A. Wait, I need to clarify: when I write (A=5,C=8), I mean Box A is at position 5 and Box C is at position 8. So position 5 is occupied by Box A. The answer is A.

Question 7

Six colored boxes are stacked in a tower with positions 1 (bottom) to 6 (top). The conditions are:
(i) The Red box is 3 positions above the Blue box.
(ii) The Green box is immediately below the Yellow box.
(iii) The Pink box is at an even position.
(iv) The Orange box is not adjacent to the Red box.

If Blue is at position 2, which position is the Green box?

Accepted Answer

Given Blue at position 2, condition (i) places Red at position 5 (2+3). Condition (ii) requires Green immediately below Yellow, so they occupy consecutive positions. Condition (iii) restricts Pink to positions 2, 4, or 6. Since Blue is at 2, Pink is at 4 or 6. Condition (iv) states Orange is not adjacent to Red (position 5), so Orange cannot be at 4 or 6. Remaining positions for Green-Yellow pair: (1,2), (3,4), (4,5), (5,6). Position 2 is Blue, position 5 is Red. Valid pairs: (1,2)—no, 2 is Blue; (3,4)—possible; (4,5)—no, 5 is Red. So Green=3, Yellow=4. Pink must be at 6 (even, not 4 since Yellow=4). Orange at 1. Verify (iv): Red at 5, Orange at 1—not adjacent ✓.

Question 8

Seven boxes are arranged in a vertical stack (positions 1–7, bottom to top). The clues are:
(i) Box M is exactly 2 positions below Box N.
(ii) Box P is immediately above Box Q.
(iii) Box L is at position 1.
(iv) Box R is at an odd position and not at position 1.
(v) Box S is not adjacent to Box M.

Which box is at position 4?

Accepted Answer

From (iii), L = 1. From (i), M and N are 2 apart: (M,N) ∈ {(2,4), (3,5), (4,6), (5,7)}. From (ii), P and Q are consecutive. From (iv), R ∈ {3, 5, 7}. Remaining boxes: M, N, P, Q, R, S in positions 2–7. Test (M,N) = (2,4): Positions {3,5,6,7} for P,Q,R,S. R ∈ {3,5,7}. P-Q consecutive in {3,5,6,7}: (3,4)—no, 4 is N; (5,6), (6,7). If P=5,Q=6, then R ∈ {3,7}, S ∈ {3,7}. If R=3, S=7. Check (v): M=2, S=7—not adjacent ✓. If P=6,Q=7, then R ∈ {3,5}, S ∈ {3,5}. If R=3, S=5. Check (v): M=2, S=5—not adjacent ✓. If R=5, S=3. Check (v): M=2, S=3—adjacent ✗. So valid: (M=2,N=4,P=5,Q=6,R=3,S=7) or (M=2,N=4,P=6,Q=7,R=3,S=5). Both have position 4 = N. Verify other (M,N) pairs lead to contradictions with (v). Position 4 = N.

Question 9

Nine boxes are stacked in positions 1–9 (bottom to top). The conditions are:
(i) Box A is 4 positions below Box C.
(ii) Box B is immediately above Box D.
(iii) Box E is at position 5.
(iv) Box F is at an odd position greater than 5.
(v) Box G is not adjacent to Box A.

If Box A is at position 2, which box is at position 6?

Accepted Answer

From (iii), E = position 5. From (i) and given A = position 2, C = position 6 (2+4). From (ii), B and D are consecutive with B above D. From (iv), F ∈ {7,9}. Remaining boxes: B, D, F, G, H, I at positions {1,3,4,7,8,9}. From (ii), B-D consecutive pairs in {1,3,4,7,8,9}: (1,2)—no, 2 is A; (3,4), (7,8), (8,9). From (v), E at 5. From (iv), F ∈ {7,9}. Test F=7: B-D ∈ {(3,4), (8,9)}. If B=3,D=4: positions {1,8,9} for {G,H,I}. From (v), A=2. Check (v): A=2, G ∈ {1,8,9}. If G=1, distance=1, adjacent ✗. If G=8 or 9, not adjacent ✓. If B=8,D=9: positions {1,3,4} for {G,H,I}. From (v), A=2, G ∈ {1,3,4}. If G=1, distance=1, adjacent ✗. If G=3, distance=1, adjacent ✗. If G=4, distance=2, not adjacent ✓. Valid: (A=2,C=6,E=5,F=7,B=3,D=4,G∈{8,9}) or (A=2,C=6,E=5,F=7,B=8,D=9,G=4). Both have position 6 = C.

Question 10

Ten boxes are arranged in a vertical stack (positions 1–10, bottom to top). The conditions are:
(i) Box V is 5 positions below Box W.
(ii) Box X is immediately above Box Y.
(iii) Box Z is at position 1.
(iv) Box U is at an even position and not at position 10.
(v) Box T is not adjacent to Box V.

If Box V is at position 3, which box is at position 8?

Accepted Answer

From (iii), Z = position 1. From (i) and given V = position 3, W = position 8 (3+5). From (ii), X and Y are consecutive with X above Y. From (iv), U ∈ {2,4,6,8}. But position 8 = W, so U ∈ {2,4,6}. Remaining boxes: X, Y, U, T, S, R, Q, P at positions {2,4,5,6,7,9,10}. From (ii), X-Y consecutive in {2,4,5,6,7,9,10}: (4,5), (5,6), (6,7), (9,10). From (iv), U ∈ {2,4,6}. From (v), T not adjacent to V (position 3), so T ∉ {2,4}. Test U=2: X-Y ∈ {(4,5), (5,6), (6,7), (9,10)}. If X=4,Y=5: positions {6,7,9,10} for {T,S,R,Q}. From (v), T ∉ {2,4}, so T ∈ {6,7,9,10} ✓. If X=5,Y=6: positions {4,7,9,10} for {T,S,R,Q}. From (v), T ∈ {4,7,9,10}. But T ∉ {2,4}, so T ∈ {7,9,10} ✓. Multiple valid configurations exist, but all have position 8 = W.

SSC MTS Box / Stack Puzzle

SSC MTS Box / Stack Puzzle — Past Exam Questions

Box / Stack Puzzle— Rules & Concept

Key Points to Remember

Exam-Specific Tips

60-Second Revision — Box / Stack Puzzle