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?
Analyzing the Stacked Boxes Logic Puzzle
This puzzle involves arranging seven boxes (E, F, G, H, S, T, U) in a stack based on several conditions. We need to find the box positioned fourth from the top.
Understanding the Clues
- There are 7 boxes in total: E, F, G, H, S, T, U.
- Condition 1: Four boxes are between H and E. This implies a separation of 6 positions (e.g., H _ _ _ _ E or E _ _ _ _ H).
- Condition 2: Only S is kept above H. This means S must be in a position higher than H, and in typical logic puzzles like this, it implies S is immediately above H, forming a block: SH.
- Condition 3: Two boxes are between F and U. This implies a separation of 4 positions (e.g., F _ _ U or U _ _ F).
- Condition 4: T is kept immediately above G. This forms a block: TG.
- Condition 5: U is not kept immediately above T. The sequence UT is forbidden.
Step-by-Step Solution Derivation
Step 1: Combining Core Constraints
We have two fixed blocks: SH (from Condition 2) and TG (from Condition 4). We also know there are 4 boxes between H and E (Condition 1). Let's combine SH with Condition 1.
This gives two primary possible structures for the entire stack of 7 boxes:
- Structure A: Starts with SH, ends with E, with 4 boxes in between. Sequence: S H _ _ _ _ E
- Structure B: Starts with E, ends with HS, with 4 boxes in between. Sequence: E _ _ _ _ H S
Step 2: Evaluating Structure A (S H _ _ _ _ E)
The 4 empty slots (positions 3, 4, 5, 6) must contain the remaining boxes: F, G, T, U.
We need to place the TG block and satisfy the condition of 2 boxes between F and U (F _ _ U or U _ _ F). Since there are exactly 4 slots available, F and U must be at the ends of these slots.
- Possibility A1 (F _ _ U): Place F at position 3 and U at position 6. The arrangement is S H F _ _ U E. The TG block must fit in slots 4 and 5. Result: S H F T G U E.
- Check Constraint 5 (U not immediately above T): In this arrangement, U is below T. This is valid.
- All other constraints are met by the structure. This is a VALID arrangement.
- Possibility A2 (U _ _ F): Place U at position 3 and F at position 6. The arrangement is S H U _ _ F E. The TG block must fit in slots 4 and 5. Result: S H U T G F E.
- Check Constraint 5 (U not immediately above T): U is immediately above T. This violates the constraint. This is INVALID.
From Structure A, the only valid order is S, H, F, T, G, U, E (from top to bottom).
Step 3: Evaluating Structure B (E _ _ _ _ H S)
The 4 empty slots (positions 2, 3, 4, 5) must contain F, G, T, U.
Again, we need to fit the TG block and satisfy F _ _ U or U _ _ F within these 4 slots.
- Possibility B1 (F _ _ U): Place F at position 2 and U at position 5. The arrangement is E F _ _ U H S. The TG block fits in slots 3 and 4. Result: E F T G U H S.
- Check Constraint 2 (Only S is kept above H): In this arrangement, S is at position 7 and H is at position 6. S is *below* H, not above. This violates Condition 2. This is INVALID.
- Possibility B2 (U _ _ F): Place U at position 2 and F at position 5. The arrangement is E U _ _ F H S. The TG block fits in slots 3 and 4. Result: E U T G F H S.
- Check Constraint 5 (U not immediately above T): U is immediately above T. This violates the constraint. This is INVALID.
Structure B does not yield any valid arrangements.
Step 4: Identifying the Box Fourth from the Top
The only arrangement consistent with all the clues is the one derived from Structure A:
| Position | Box |
| 1 (Top) | S |
| 2 | H |
| 3 | F |
| 4 | T |
| 5 | G |
| 6 | U |
| 7 (Bottom) | E |
The question asks for the box that is fourth from the top. In the determined order (S, H, F, T, G, U, E), the box at the 4th position is T.
Important Questions from Puzzle (Notes)
- Four individuals - P, Q, R and S - are suspects in a theft case. They make the following statements :
P says: "Q is guilty."
Q says: "R is guilty."
R says: "P is innocent."
S says: "I am innocent"
If it is known that exactly one of them is guilty, and only the guilty person lies (all innocent people tell the truth), then who is the guilty one? - 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: - Read the following informations and answer the question given below :
A total of nine cards consisting of four kings, four queens and one joker are distributed among three persons P, Q and R such as :
I. Q has two cards, P has three cards and R has four cards.
II. Person, who has maximum number of cards, does not have the joker.
III. Each one has atleast one king while Q has two kings.
Who has three queens ? Consider the following information regarding a 3-digit PIN.
The correct PIN is- A boatman on a bank of a river has to carry a dog, a cat and a container full of milk to the other bank in a boat, one at a time. The cat cannot be left alone with the milk or with the dog on either bank. What is the minimum number of times the boatman has to cross the river to carry all to the other bank?
