# Blood relations in deducing family tree

Eight members of a family A,B,C,D,E,F,G and H are sitting around a circular table. Some of them are facing inside and some of them are facing outside.

• The couples are facing inside and singles are facing outside.
• E is the daughter of C, who is sitting second to the right of her husband
• B is sitting opposite to his father and facing outside
• G is the sister-in law of both H and E and also she is not immediate neighbour of neither H or E
• D is sitting between C and G, and is the only group of three females sitting together
• H is facing his Mother C and G is facing her father in Law A
• E is the only daughter in the family and sitting second to the right of her nephew

How can I deduce the family tree and seating arrangement around the circular table?

I have tried

Family Tree:

From the 1st statement, we deduce E is the female and his mother is C

From the 3rd statement, G is sister-in-law of both H and E

E and H is married to one person and his sister is E, but we don't know the gender of H or E from 3rd statement

From the 6th statement, H is facing his mother C and G is facing her father-in-law A

Now we know H is the male and married to a female, and her sister is G. G is married to a male and his father is A

E is the only daughter and sitting second to the right of her nephew, from this E is brother son is there

I cannot deduce the family tree, how can this be done?

• Your sister-in-law can either be your spouse's sister, or the wife of your sibling. So "Now we Know H is the Male and married to female and her sister is G" isn't necessarily correct - H could be a male (married because he is facing inward) whose brother is married to G. Apr 2, 2017 at 21:59

Here's my attempt:

Let's assume the positions on the table are the wind directions (N, NE, E, ...)

Let's start with saying that $C$ is sitting east.

Statement 2: C is facing inward, since her husband is also present. So her husband is sitting south, again facing inward.

Statement 7, we gather that H is sitting on the western spot, facing inward. This means he must be married.

Statement 5: D is sitting between C and G. Since C sits to the east, and the south spot is C's husband, this means G must be north and D northeast.

Statement 6: A is south. Statement 3: B is sitting opposite to his father and facing outside. The only way they can be opposite eachother, is if F is the father and they occupy north-west and south-east. This means E must be south-west.

Statement 4: G is the sister-in law of both H and E. But G is facing inward, so must have a partner. However, it can't be B (facing outward), A (C's partner) or H (she's his sister-in-law), so G must be a couple with F; who's then facing inward.

At this point, H still needs a partner, and only D and E are left as possibilities. But E is H's sister, so the partner must be D. This also means D is facing inward.

Finally, E must be looking outward because there's nobody left to form a couple with.

Note that G being the sister-in-law then implies that G and D are sisters.

Statement 7: E is second to the right of her nephew. Since F is the partner of G, who's E's sister in law, the nephew in question has to be B. So B is sitting north-west, and F is sitting south-east.

Final results:

North: G, inward.
North-east: D, inward.
East: C, inward.
South-east: F, inward.
South: A, inward.
South-west: E, outward.
West: H, inward.
North-west: B, inward.

• root , G is a sister in law of both H and E , both H and E is married persons, but in E is not married How ? is it possible @steamy root Apr 2, 2017 at 17:20
• please deduce the family tree first from given data, then we will plot into the circular arrangement Apr 2, 2017 at 17:27
• "Note that G being the sister-in-law then implies that G and D are sisters." - if that were the case E would be G's sister's husband's sister, which isn't normally classed as a sister-in-law. Isn't it F, H and E are siblings, with G married to F, and thus G is the sister-in-law of H and E? Apr 2, 2017 at 21:39
• @Learninguser - You can't deduce the family tree without concurrently deducing the circular arrangement as SteamyRoot has done. Apr 2, 2017 at 21:41

My deduction:

From the first, second and sixth statements:
H and E are Brother-Sister
C is their Mother

From the fourth statement:
G is the wife of a third brother to H and E; it's either B or F.

From third statement: G is the mother of B and wife of F because B is single.

From sixth statement: A is the father of F and therefore the father of H and E.

H's wife is D because it can't be C "his mother", E "his sister " or G "his sister in law".
So we can deduce that G and D are sisters.

E is supposed to be single because there are four women according to the fifth statement: C, D, G and E.  So there are four men: two are her brothers according to the fourth and sixth statements, one is her father according to the second statement and one is her nephew according to the final statement.

F is the brother of H and E because it's the only way "in my opinion" for G to be the sister-in-law to E. That G is the wife of E's sibling.

My answer is – according to compass directions:

North: B "Son of F" Outside

North-east: G "wife of F" Inside

North-West: H "Son of C and A, Husband of D" Inside

East: D wife of H

South-East: C "Mother of H, F, E" Inside

South: F "Brother of E and H, Son of C and A, Husband of G" Inside

South-West: A "Father of H, F, E" Inside

West: E "The only daughter" Outside
North: B "Son of F" Outside

North-east: G "wife of F" Inside

North-West: H "Son of C and A, Husband of D" Inside

East: D wife of H

South-East: C "Mother of H, F, E" Inside

South: F "Brother of E and H, Son of C and A, Husband of G" Inside

South-West: A "Father of H, F, E" Inside

West: E "The only daughter" Outside