Floor Arrangement Puzzle Explained
We need to determine the number of people living between floor 5 (H) and floor 1 (K) based on the given clues.
Analyzing Constraints and Deductions
- Building has 6 floors, numbered 1 (lowest) to 6 (topmost).
- People: L, K, H, M, Z, U.
- Clue 1: L is immediately below H. (Pair LH)
- Clue 2: Z is immediately below U. (Pair ZU)
- Clue 3: Three people live between M and Z. (Implies a 4-floor gap: M _ _ _ Z or Z _ _ _ M)
- Clue 4: K is not on floor 6.
- Clue 5: H's floor number \(\ge\) U's floor number.
Determining Floor Occupancy
Let's combine Clue 2 (ZU pair) and Clue 3 (M and Z separated by 3 people):
- Scenario 1: If M is on floor 1, Z must be on floor 5 (M _ _ _ Z). Then U must be on floor 6 (immediately above Z). Floors: M(1), _, _, _, Z(5), U(6). Remaining people L, K, H must occupy floors 2, 3, 4. Clue 1 (LH pair) means L(2)H(3) or L(3)H(4). However, Clue 5 (H's floor \(\ge\) U's floor) fails because U is on floor 6, and H would be on floor 3 or 4. Thus, Scenario 1 is impossible.
- Scenario 2: If Z is on floor 2, M must be on floor 6 (Z _ _ _ M). Then U must be on floor 3 (immediately above Z). Floors: _, Z(2), U(3), _, _, M(6). Remaining people L, K, H must occupy floors 1, 4, 5. Clue 1 (LH pair) means L must be on floor 4 and H on floor 5. Floors: L(4), H(5). Clue 5 (H's floor \(\ge\) U's floor) holds because H(5) \(\ge\) U(3). Clue 4 (K not on floor 6) holds. The only remaining floor for K is floor 1.
The derived arrangement is:
| Floor 6 | M |
| Floor 5 | H |
| Floor 4 | L |
| Floor 3 | U |
| Floor 2 | Z |
| Floor 1 | K |
Calculating People Between H and K
H lives on floor 5 and K lives on floor 1.
The people living on floors between 1 and 5 are on floors 2, 3, and 4.
From the arrangement, Z lives on floor 2, U lives on floor 3, and L lives on floor 4.
Therefore, there are 3 people (Z, U, L) living between H and K.
Similar Questions
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Important Questions from Floor Puzzle
- If P is on the first step, on which step is S?
- If P is on the first step, which of the following is true?
- If T was on the third step, which of the following pairs is incorrect?
If T joined P, Q, R and S, and T was on the third step, and Q was on a higher step than T, which step must be vacant?
If there are two steps in between the steps on which A and D are standing and C is standing on Step 6, A must be standing on which of the following steps?
