Prove the family path
Exam puzzles describe a whole family in a few sentences, then ask about two people far apart in it. In this lesson you draw the family once, as rows of generations, and prove every answer with a path of links that the clues really state.
Guess first
In a family of six, A is the father of B and C. B is a woman, and D is her husband. C is a man, and E is his daughter. F is the son of B and D. How is E related to F?
Show answer
Correct answer: A
From F: his mother B, her brother C (both are A's children, and C is a man), and C's daughter E. So E is the daughter of F's mother's brother: his ममेरी बहन.
Option B: E and F have different parents (C, and B with D), so they are cousins, not brother and sister.
Option C: E is B's niece: B's brother's daughter. The question asks about F, one rung below B.
Option D: F's link runs through his mother B, not his father D.
Hint: Climb from F one stated link at a time.
Six people, five sentences, and the answer needed three of them in the right order. A drawing that puts everyone in place first makes that order easy to find.
Draw it once
A family puzzle is a seating plan.
Rows generations
grandparents on top, then parents, then children
Seats side by side couples, brothers and sisters
on the same row
A line down parent to child
the only way to change rows
A ticket for each answer the path
every link must come from a clue
| The clue says | Draw this |
|---|---|
| X is the father of Y | X one row above Y, with a line down; X is a man |
| X is the wife of Y | X beside Y on the same row; X is a woman |
| X is the son of Y and Z | one line from the couple Y and Z down to X; X is a man |
| X is the father of Y and Z | Y and Z on one row, brothers or sisters, with the same parents |
A name never gives a gender here: only words such as father, sister, wife or son do.
See it: the family of six as a plan
flowchart TD A["A: man"] --> B["B: woman, married to D"] A --> C["C: man"] B --> F["F: son of B and D"] C --> E["E: daughter of C"]
Three rows: A on top; B, her husband D and C in the middle; E and F at the bottom. Now every answer is a walk along the lines, and every step of the walk points to a clue.
Prove a path:
- Start from the person after "related to".
- Take one link at a time, and name the clue that gives it.
- Brothers and sisters share parents: "A is the father of B and C" links B and C.
- Name the end of the walk, using only genders the clues give.
Try it on paper. Draw your own family as rows of generations. Write next to each line the sentence a puzzle would use for it.
Find the rule
In the family of six above, how many generations are there?
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Correct answer: A
A is on the top row. B, her husband D and her brother C share the middle row. E and F are on the bottom row. Three rows: three generations.
Option B: Two is the number of steps from the top row to the bottom row. The question counts the rows.
Option C: D married into the family, but he belongs on B's row, not on a row of his own.
Option D: Every person can be placed on a row from the clues.
Hint: Draw the rows and count them, not the steps between them.
P is the mother of Q and R. Q is married to S, and T is the child of Q and S. R is a man. Which statement is certain?
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Correct answer: A
R is the brother of T's parent Q, so R is T's uncle. Q's gender is not given, so we cannot say which side.
Option B: "Maternal" makes Q T's mother; no clue says Q is a woman.
Option C: No clue gives S's gender: S may be T's mother.
Option D: "Paternal" makes Q T's father; Q's gender is not given.
Hint: For each statement, find the gender it needs, then look for the clue that gives it.
Name the rule
Draw once, prove every link.
- Draw the rows first: each parent one row above the child; couples, brothers and sisters side by side.
- Answer by a walk from the person after "related to", one link at a time.
- Every link must point to a clue: a parent, a child, a brother or sister, a spouse.
- A gender or a side that no clue gives stays open, and the answer must say so.
In a crowded family the mind fills gaps by habit: a name taken as a gender, two people on the same row taken as brother and sister. Naming the clue behind each link takes a moment and stops the habit before it costs marks.
Worked, half-done, solo
Question
(1) K's son L has a wife, M. (2) Their children are N, a girl, and O, a boy. (3) O's wife is P, and Q is the son of O and P. How is Q related to K?
Solution
- Draw the rows
Row 1: K. Row 2: L and his wife M. Row 3: N, O and O's wife P. Row 4: Q.
- Walk from K
K's son is L (clue 1). L's son is O (clue 2: O is a boy, a child of L and M). O's son is Q (clue 3).
- Name it
Three rungs down through sons: a great-grandson, परपोता.
Answer: Q is K's great-grandson.
Watch out: M, N and P are on the plan but not on the path. A walk uses only the links it needs.
Now finish one that is half done.
In the family of K above, how is N related to P? Walk from P: her husband O (clue 3), then O's sister N (clue 2: N and O are L and M's children, and N is a girl). So N is P's ...
Show answer
Correct answer: A
P's husband is O, and N is O's sister: N is the sister of P's husband, P's ननद.
Option B: N is O's sister, not P's. This drops the marriage.
Option C: Brother's wife (भाभी) is P as seen from N: the reverse question.
Option D: A wife's sister is a husband's word. P's link runs through her husband.
Hint: Cross the marriage first: whose sister is N?
And one on your own.
G and H are husband and wife. They have two children, I and J. I is a woman and J is a man. J's wife is K, and L is the daughter of J and K. How is L related to I?
Show answer
Correct answer: A
From I: her brother J (both are G and H's children, and J is a man), then J's daughter L. So L is I's brother's daughter: her niece, भतीजी.
Option B: L is J's daughter, not I's. This drops the first link.
Option C: L's parent in the middle is J, a man: the brother, not a sister.
Option D: Paternal aunt (बुआ) is I as seen from L: the reverse question.
Hint: Walk from I: which clue links her to L's parent?
The traps
- A gender from a name: only words such as father, wife, son or sister give a gender.
- Siblings from the same row: two people on one row are brothers or sisters only if a clue gives them a shared parent.
- A link from habit: every step of the walk must point to a clue.
- Steps counted instead of rows: a family with three rows has three generations.
- A person who married in, left out: count them in their partner's row.
In the family of K above, Dev was asked how M is related to Q. He said: "M is Q's नानी." What went wrong?
Show answer
Correct answer: A
From Q: his father O (clue 3), then O's mother M (clues 1 and 2: M is L's wife, and O is their child). So M is Q's father's mother, his दादी. नानी is the mother's mother.
Option B: The count is right: M is two rungs above Q.
Option C: The reverse would describe Q as seen from M: her grandson.
Option D: Q's walk to M starts with his father, so the word is दादी.
Hint: Through which parent does Q's walk to M start?
Mixed check
In a code, A @ B means "A is the father of B", A # B means "A is the mother of B", A % B means "A is the brother of B" and A & B means "A is the sister of B". Which expression means "A is the maternal grandmother of B"?
Show answer
Correct answer: A
A # X: A is X's mother. X # B: X is B's mother. So A is the mother of B's mother: B's maternal grandmother, नानी.
Option B: X @ B makes X B's father, so A would be the paternal grandmother.
Option C: A @ X makes A a father, so A would be the maternal grandfather.
Option D: This says B is A's maternal grandmother: the statement is turned around.
Hint: Lesson 10: read each option back as two sentences.
Pointing to a girl in a photo, Mahesh said: "Her father is the only son of my father." Mahesh is a man. How is the girl related to Mahesh?
Show answer
Correct answer: A
The only son of Mahesh's father is Mahesh himself, since Mahesh is a man. So the girl's father is Mahesh: she is his daughter.
Option B: That needs another son of Mahesh's father, but "only son" leaves no one else.
Option C: Father is Mahesh as seen from the girl: the reverse question.
Option D: "Only son" and "Mahesh is a man" fix the answer.
Hint: Lessons 3 and 4: who is the only son of Mahesh's father?
Quick reference
Family puzzles
- Draw
- rows of generations; couples, brothers and sisters side by side parent one row above the child
- Walk
- from the person after "related to", one link at a time F, his mother B, her brother C, his daughter E
- Prove
- every link points to a clue no link from habit, no gender from a name
- Count
- generations = rows someone who married in sits on the partner's row
- Open
- a gender or a side no clue gives say "uncle", not "maternal uncle"
Why it works: the plan holds every clue in one place, and the walk uses only stated links, so an answer can be checked step by step.
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