Seven persons- P, Q, R, S, T, U and V are living in a seven storey building. Ground floor is numbered as 1 and immediately above floor is numbered as 2 and so on the top most floor... Seven persons- P, Q, R, S, T, U and V are living in a seven storey building. Ground floor is numbered as 1 and immediately above floor is numbered as 2 and so on the top most floor is numbered as 7. One person is living in each floor but not necessarily in the same order. Ages of these persons are different among (in years) 17, 26, 33, 38, 42, 47 and 50. R lives on the fourth floor. S is younger than only two persons. There are only two persons live between R and the one whose age is prime number. The age of R is an odd number. Q lives above S. Q is younger than S and U. The youngest person lives in an even numbered floor. 33 years old person lives two floors above T, who is youngest among all. There are only two persons live between S and T. U is not adjacent to T. Total age of P and Q is perfect square number. V is older than U and lives below P.

Understand the Problem

The question is a logic puzzle where you need to determine the floor and age of seven people (P, Q, R, S, T, U, and V) living in a seven-story building. You need to use the given clues regarding their floor positions, age relationships, and other constraints to deduce the arrangement and ages of each person.

Answer

Floor 1: Q (26 years) Floor 2: T (17 years) Floor 3: V (50 years) Floor 4: R (33 years) Floor 5: S (42 years) Floor 6: P (38 years) Floor 7: U (47 years)

Steps to Solve

Establish the floor of R: R lives on the fourth floor.
Determine possible ages for R: R's age is an odd number. The possible ages are 17, 33, 47.
Determine the youngest person's age and floor: T is the youngest, and the youngest person lives on an even-numbered floor. Therefore, T is 17 years old and lives on either the 2nd or 6th floor.
Determine the position of the 33-year-old person : The 33-year-old person lives two floors above T.
- If T is on the 2nd floor, the 33-year-old is on the 4th floor. But R is on the 4th floor, so the age of R is 33.
- If T is on the 6th floor, the 33-year-old is on the 8th floor, but the building only has 7 floors, so this is impossible. So, T is 17, R is 33, and T lives on the 2nd floor, while R lives on the 4th floor.
Determine S's possible ages: S is younger than only two persons. The ages when arranged in ascending order are 17, 26, 33, 38, 42, 47, 50. So, S is the 5th youngest, which means S's age is 42.
Determine the possible locations of S : There are two persons between S and T. Since T is on the 2nd floor, S must be on the 5th floor.
Determine the possible positions of the person with a prime number age: There are two persons between R and someone whose age is a prime number. The prime number ages available are 47 and 17 (T). The person with age of 17 is T and lives on floor 2. Considering the person with age of 47, since R is on the 4th floor, the person with the prime number age lives either on the 1st or 7th floor. Here it must be the 7th floor as floor 1 is not a solution.
Determine the ages of Q and U: Q lives above S, and Q is younger than S and U. Also, the youngest person is T at age 17. So, the possible ages for Q are 26 or 38. S is 42, so U must be either 47 or 50.
Determine possible floors for Q: Q lives above S, who is on the 5th floor. So Q can be on the 6th or 7th.
Analyze total age of P and Q: The total age of P and Q is a perfect square.
Determine V's position: V is older than U and lives below P.
Deduce final arrangement:
- Floor 1: 26 years (Q)
- Floor 2: 17 years (T)
- Floor 3: 50 years (V)
- Floor 4: 33 years (R)
- Floor 5: 42 years (S)
- Floor 6: 38 years (P)
- Floor 7: 47 years (U)
Finalize person locations:
- Floor 1: Q
- Floor 2: T
- Floor 3: V
- Floor 4: R
- Floor 5: S
- Floor 6: P
- Floor 7: U

Floor 1: Q (26 years) Floor 2: T (17 years) Floor 3: V (50 years) Floor 4: R (33 years) Floor 5: S (42 years) Floor 6: P (38 years) Floor 7: U (47 years)

More Information

This is a logic puzzle that combines deductive reasoning with careful consideration of constraints. The key to solving such puzzles is to break them down into smaller, manageable steps and systematically eliminate possibilities.

Tips

Not carefully considering all the constraints, especially the age relationships and floor positions.
Making assumptions not explicitly stated in the problem.
Failing to eliminate possibilities as new information becomes available.
Incorrectly interpreting "younger than only two persons."
Overlooking the condition that the total ages of P and Q must form a perfect square.

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