Family Age Puzzle: Identifying the Youngest Member

This question presents a logic puzzle involving a family of seven members (A, B, C, D, E, F, G) with different ages. The goal is to determine who the youngest person in the family is by carefully analyzing the given clues.

Understanding the Clues

Let's break down the information provided:

• There are seven family members: A, B, C, D, E, F, G.
• All members have different ages.
• The members are arranged from highest age to youngest.
• The age difference between consecutively arranged persons is exactly 3 years.
• E is younger than D, but E is not the youngest.
• D's age is not 55.
• B's age is 61 and is older than A.
• The youngest person's age is 46.
• G's age is less than 52.
• A is older than E and D.
• A's age is not 55.

Calculating Possible Ages

We know there are 7 members, and their ages are consecutive with a difference of 3. We are also given that the youngest person is 46.

Let the ages from youngest to oldest be $age_7, age_6, age_5, age_4, age_3, age_2, age_1$.

• The youngest age ($age_7$) is given as 46.
• Since the consecutive age difference is 3, we can find the other ages:
• $age_6 = age_7 + 3 = 46 + 3 = 49$
• $age_5 = age_6 + 3 = 49 + 3 = 52$
• $age_4 = age_5 + 3 = 52 + 3 = 55$
• $age_3 = age_4 + 3 = 55 + 3 = 58$
• $age_2 = age_3 + 3 = 58 + 3 = 61$
• $age_1 = age_2 + 3 = 61 + 3 = 64$

So, the possible ages in the family, from oldest to youngest, are: 64, 61, 58, 55, 52, 49, 46.

Deduction Process and Member Assignment

Now, let's use the clues to assign members to these ages:

1. B's Age: We are told B's age is 61. From our calculated ages, 61 corresponds to the second oldest position ($age_2$). So, B is the second oldest.
2. A's Position: We know B (61) is older than A. This means A must be younger than 61. Possible ages for A are 58, 55, 52, 49, or 46.
3. A's Age Constraint: A's age is not 55. This eliminates 55 as a possibility for A. So, A's possible ages are 58, 52, 49, or 46.
4. A is Older than D and E: A must be older than both D and E.
5. D's Age Constraint: D's age is not 55.
6. E's Position: E is younger than D, and E is not the youngest (not 46).

Let's test the possible positions for A:

• If A were 46 (the youngest), A could not be older than D and E. So A is not 46.
• If A were 49, then D and E must be younger than 49. The only age younger than 49 is 46. So, D would have to be 46. If D is 46, then E must be younger than 46, which is impossible. So A is not 49.
• If A were 52, then D must be younger than 52. Possible ages for D are 49 or 46.
  • If D=49, then E must be younger than 49. The only option is 46. But E cannot be the youngest (46). This case fails.
  • If D=46, then E must be younger than 46, which is impossible. This case also fails.
  So A is not 52.
• Therefore, A must be 58.

If A = 58 ($age_3$):

• A is older than D and E (58 > D, 58 > E).
• D's age is not 55. So D cannot be $age_4$.
• D must be younger than A (58). Possible ages for D are 55, 52, 49, 46.
• Since D's age is not 55, D can be 52, 49, or 46.
• E is younger than D, and E is not the youngest (46).
• Let's test D's possible ages:
  • If D = 46 ($age_7$): E must be younger than 46, impossible. So D is not 46.
  • If D = 49 ($age_6$): E must be younger than 49. Possible age for E is 46 ($age_7$). But E cannot be the youngest (46). So D is not 49.
  • If D = 52 ($age_5$): E must be younger than 52. Possible ages for E are 49 ($age_6$) or 46 ($age_7$). Since E is not the youngest (46), E must be 49 ($age_6$).
  This fits all conditions: A=58, D=52, E=49. (A > D, A > E, D != 55, E < D, E != 46).

Current assignments:

• $age_1$: 64 (C or F)
• $age_2$: 61 (B)
• $age_3$: 58 (A)
• $age_4$: 55 (C or F)
• $age_5$: 52 (D)
• $age_6$: 49 (E)
• $age_7$: 46 (Remaining member)

The remaining members are C, F, and G. The remaining ages are 64, 55, and 46.

We have the clue: G's age is less than 52. The available ages less than 52 are 49 and 46. Since E is 49, G must be 46.

Therefore, G's age is 46, making G the youngest person.

Conclusion

Based on the step-by-step deduction using all the provided clues, the person with the age of 46, who is the youngest, is G.