How many boxes are kept between G and F?
Solving the Seven Boxes Arrangement Puzzle
This problem involves arranging seven boxes (E, F, G, H, S, T, U) stacked vertically based on a set of given conditions. We need to find the exact number of boxes situated between box G and box F.
Analyzing the Constraints
Let's break down the rules provided:
- There are 7 boxes in total, stacked one over the other.
- H is immediately above E: This means H and E form a fixed block (HE).
- T is immediately above U: This means T and U form a fixed block (TU).
- Only F is kept above S: This implies F is the topmost box (position 7) and S is directly below it (position 6). No other box can be above S.
- Only two boxes are kept above H: This places H at the 4th position from the top.
- T is not kept at the third position from the bottom: The third position from the bottom is position 5. So, T cannot be at position 5.
Determining the Box Order
Based on the constraints, we can deduce the arrangement step-by-step:
- Constraint "Only two boxes are kept above H" places H at position 4.
- Since "H is immediately above E", E must be at position 5.
- Constraint "Only F is kept above S" places F at the top (position 7) and S at position 6.
- The partial arrangement from top to bottom (7 to 1) is: F, S, E, H, _, _, _.
- The remaining boxes to be placed are G, T, and U in positions 1, 2, and 3.
- We know "T is immediately above U" (TU block) and "T is not kept at position 5". Since E is already at position 5, this rule doesn't further restrict T's placement among 1, 2, 3.
- The TU block must occupy adjacent slots within positions 1, 2, 3. The possibilities are:
- T at position 3, U at position 2.
- T at position 2, U at position 1.
- Scenario 1: If TU are placed at positions 3 and 2 (T=3, U=2), then G must be at position 1. The stack is: F(7), S(6), E(5), H(4), T(3), U(2), G(1).
- Scenario 2: If TU are placed at positions 2 and 1 (T=2, U=1), then G must be at position 3. The stack is: F(7), S(6), E(5), H(4), G(3), T(2), U(1).
Let's check the constraint "T is not kept at the third position from the bottom (position 5)". In both scenarios, E is at position 5, so this condition is met.
Representing the Final Arrangement
Let's represent the positions from top (7) to bottom (1):
| Position | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
| Scenario 1 Box | F | S | E | H | T | U | G |
| Scenario 2 Box | F | S | E | H | G | T | U |
Calculating Boxes Between G and F
The question asks how many boxes are kept between G and F.
- In Scenario 1: F is at position 7, G is at position 1. The boxes between them are S, E, H, T, U. The count is 5.
- In Scenario 2: F is at position 7, G is at position 3. The boxes between them are S, E, H. The count is 3.
Since "Three" is one of the options provided, Scenario 2 represents the intended solution.
Final Arrangement and Answer
The confirmed arrangement from top to bottom is F, S, E, H, G, T, U.
- Position 7: F
- Position 6: S
- Position 5: E
- Position 4: H
- Position 3: G
- Position 2: T
- Position 1: U
Box F is at the 7th position and Box G is at the 3rd position.
The boxes located between F and G are those at positions 6, 5, and 4, which are S, E, and H, respectively.
Therefore, there are 3 boxes kept between G and F.
Important Questions from Puzzle (Notes)
- 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 the same order. Only H is kept above E. Only T is kept between E and S. Only F is kept below U.
How many boxes are kept between G and F? Seven boxes E, F, G, H, S, T and U are kept one over the other but not necessarily in the same order. Only four boxes are kept between H and E. Only S is kept above H. Only two boxes are kept between F and U. T is kept immediately above G. U is not kept immediately above T. Which box is kept fourth from the top?
- Seven boxes E, F, G, H, S, T and U are kept one over the other but not necessarily in the same order. Only H is kept above E. Only T is kept between E and S. Only F is kept below U.
How many boxes are kept between G and F? What is the minimum number of moves required to transform figure 1 to figure 2? A move is defined as removing a coin and placing it such that it touches two other coins in its new position.
