I asked five people the following six questions:
- What colour are Maddy's eyes?
- What is the cat's name?
- How old is George?
- Who is Fiona's favourite author?
- Where does Uncle Bill keep his guitar?
- Is Pete teetotal?
And I received the following answers:
Maddy: 1. Black, 2. Fluffy, 3. 40, 4. Dickens, 5. Study, 6. Yes.
Helen: 1. Green, 2. Snowy, 3. 41, 4. Hemingway, 5. Study, 6. No.
George: 1. Blue, 2. Tiddles, 3. 43, 4. Hemingway, 5. Bedroom, 6. Yes.
Fiona: 1. Grey, 2. Fluffy, 3. 40, 4. Hemingway, 5. Dining Room, 6. No.
Pete: 1. Grey, 2. Tiddles, 3. 43, 4. Shakespeare, 5. Dining Room, 6. Yes.
Each of the five people questioned have answered two questions truthfully and four questions untruthfully. Furthermore, every question has been answered truthfully by at least one person.
What facts can be deduced with certainty?
It can be found that there are two sets of answers that are consistent with each other, as follows:
Maddy answered 3 & 5, Helen 5 & 6, George 1 & 2, Fiona 3 & 6 and Pete 2 & 4.
Maddy answered 2 & 5, Helen 5 & 6, George 1 & 3, Fiona 2 & 6 and Pete 3 & 4.
So we know that Maddy and Helen's answer to question 5, Helen and Fiona's answer to question 6, George's answer to question 1 and Pete's answer to question 4 are truthful.
Maddy's eyes are Blue,
Fiona's favourite author is Shakespeare,
Uncle Bill's guitar is in the Study and
Pete is not Teetotal.
We also know that the cat's name is not Snowy and George is not 41.