How many boxes are kept between G and F?
Solving the Seven Boxes Arrangement Puzzle
This problem requires us to figure out the arrangement of seven boxes stacked vertically based on given clues and then count how many boxes lie between box G and box F.
Understanding the Clues
First, let's list the boxes and the constraints:
- Boxes: E, F, G, H, S, T, U (7 total).
- Arrangement: Stacked one over the other.
- Clue 1: "Only H is kept above E." This strongly suggests that H is positioned immediately above E. We can represent this unit as $HE$.
- Clue 2: "Only T is kept between E and S." This means T is directly between E and S, forming either the sequence $ETS$ or $STE$. Since Clue 1 established that H is above E, the sequence must be $ETS$. Combining this with Clue 1, we get a block of four boxes: $HETS$.
- Clue 3: "Only F is kept below U." Similar to Clue 1, this implies U is positioned immediately above F. We can represent this unit as $UF$.
Constructing Possible Arrangements
From the clues, we have deduced two fixed blocks:
- Block A: $HETS$
- Block B: $UF$
The box G is the only remaining item to place. We have 7 positions in the stack.
We need to arrange these three components (Block A, Block B, and G) while keeping the internal order of boxes within Block A and Block B intact.
Scenario 1: Block B ($UF$) is placed above Block A ($HETS$).
This forms a base structure of $UF HETS$ (6 boxes). Now, we must place G.
- Arrangement 1.1: G at the top.
Stack (Top to Bottom): $G U F H E T S$
Positions: 1(G), 2(U), 3(F), 4(H), 5(E), 6(T), 7(S).
Boxes between G (Pos 1) and F (Pos 3): U. Count = 1. - Arrangement 1.2: G between UF and HETS.
Stack (Top to Bottom): $U F G H E T S$
Positions: 1(U), 2(F), 3(G), 4(H), 5(E), 6(T), 7(S).
Boxes between G (Pos 3) and F (Pos 2): None. Count = 0. - Arrangement 1.3: G at the bottom.
Stack (Top to Bottom): $U F H E T S G$
Positions: 1(U), 2(F), 3(H), 4(E), 5(T), 6(S), 7(G).
Boxes between G (Pos 7) and F (Pos 2): H, E, T, S. Count = 4.
Scenario 2: Block A ($HETS$) is placed above Block B ($UF$).
This forms a base structure of $HETS UF$ (6 boxes). Now, we must place G.
- Arrangement 2.1: G at the top.
Stack (Top to Bottom): $G H E T S U F$
Positions: 1(G), 2(H), 3(E), 4(T), 5(S), 6(U), 7(F).
Boxes between G (Pos 1) and F (Pos 7): H, E, T, S, U. Count = 5. - Arrangement 2.2: G between HETS and UF.
Stack (Top to Bottom): $H E T S G U F$
Positions: 1(H), 2(E), 3(T), 4(S), 5(G), 6(U), 7(F).
Boxes between G (Pos 5) and F (Pos 7): U. Count = 1. - Arrangement 2.3: G at the bottom.
Stack (Top to Bottom): $H E T S U F G$
Positions: 1(H), 2(E), 3(T), 4(S), 5(U), 6(F), 7(G).
Boxes between G (Pos 7) and F (Pos 6): None. Count = 0.
Final Conclusion
By analyzing all possible valid arrangements derived from the clues, we found the number of boxes between G and F could be 0, 1, 4, or 5.
The options provided were 1, 2, 3, and 4.
The scenarios resulting in exactly One box between G and F are Arrangement 1.1 ($G U F H E T S$, where U is between G and F) and Arrangement 2.2 ($H E T S G U F$, where U is between G and F).
Therefore, based on the deductions, the number of boxes kept between G and F is One.
Important Questions from Puzzle (Notes)
- There are five men - A, B, C, D and E, six women P, Q, R, S, T and Z. A, B, and R are advocates. S, Q, P, D and C are doctors and the rest are teachers. A team has to be selected from these eleven persons subject to the following conditions:
(I) A, P and Z have to be together.
(II) B cannot go with D or R.
(III) E and Q have to be together.
(IV) C and T have to be together.
(V) D and P cannot go together.
(VI) C cannot go with Q.
If the team formed consists of two male advocates, two lady doctors and one teacher, the members of the team can be: - Seven boxes S, F, G, H, T and U are kept one over the other but not necessarily in the same order. Only two boxes are kept below S. Only one box is kept above U. Only one box is kept between U and B. G is kept immediately above F. T is kept at some place below H.
How many boxes are kept between H and G? - Seven boxes E, F, G, H, S, T and U are kept one over the other but not necessarily in themsame order. No box is kept above E. Only three boxes are kept between E and U. Only one box is kept between G and H. H is kept immediately above U. Only four boxes are kept between G and F. T is kept at some place above S. Which box is kept second below T?
- Seven boxes E, F, G, H, S, T and U are kept one over the other but not necessarily in the same order. H is kept immediately above E. T is kept immediately above U. Only F is kept above S. Only two boxes are kept above H. T is not kept at third position from the bottom.
How many boxes are kept between G and F? - Seven boxes A, B, C, D, E, F and G are kept one over the other but not necessarily in the same order.
Only two boxes are kept between D and E. Only F is kept above C. No box is kept below E. G is kept at some place below A but at some place above B.
How many boxes are kept below B?
