Who are you in this crazy family?

Logic Level 2

In a family of 5 members formed by Lily, Mery, John, Sara and Ana we know that John is Lily's biological grandfather. We also know that John and Lily are the oldest and youngest of this family and that the sequence of relatives must be lineal , that is we can't jump from the grandfather to the granddaughter without having more relatives . Each member tells this:

1. Ana: "Sara is my twin and I'm telling the truth."

2. Sara: "Mery is my daughter."

3. John: "Mery is my wife."

4. Lily: "Mery isn't telling the truth and she is my grandmother."

5. Mery: "John is lying."

We know that 3 of this statements are true and 2 of them are false. We assume that for a person's statement to be true, their two claims must be true. However, for a person's statement to be false at least one of the claims of that person must be false.

Who is Lily's mother?

Mery Mery or Ana Ana We can't tell for sure Ana or Sara Sara or Mery Sara

Andrea P by Andrea P , 18, Spain

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1 solution

Sree Narayanan
Apr 5, 2020

Let's arrange the family in the form of a list from 1-5 in descending order of their age.

  1. John (We were told that John is the oldest and is the grandfather of Lily)
  2. _
  3. _
  4. _
  5. Lily (Given that she's the youngest and is the granddaughter of John)

From the given information, we can determine this much, and we know it's a linear sequence.

We know that 3 of these statements are true and 2 of them are false, so let's assume John is telling the truth. That automatically means Mery is lying, and Lily is telling the truth(both her statements are true). Now the list would look like this:

  1. John
  2. Mery
  3. _
  4. _
  5. Lily

Now, if we look at Sara's statement, it doesn't logically fit into the sequence as she cannot be older than John to be Mery's mother. So her statement is false, and Ana is telling the truth. Now the list would look like this:

  1. John
  2. Mery
  3. Ana/Sara (it's interchangeable as they are twins, and it doesn't matter who's older)
  4. Sara/Ana
  5. Lily

Now, we can tell Lily's mother is either Ana or Sara, but we cannot be sure as there is no information given which states it or which we can deduce from.

So it's Ana or Sara (or even Ana and Sara cause we are in a 2020 world :p)

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