Blood Relations: Logical Reasoning Notes for NSO (Science Olympiad)

Blood Relations – Logical Reasoning (Science Olympiad)

Goal – From a set of clues, deduce the exact parent‑child or sibling relationships among a group of people.

1. Simple Explanation

In “Blood Relations” puzzles you are given a list of statements such as
“A is the father of B.” or “C is the sibling of D.”
You must reconstruct the family tree (who is the parent of whom, who are siblings, who are married, etc.) so that every statement is true.

2. Key Points

Concept	What it means	Why it matters
Parent/Child	A direct line of descent (father/mother → child).	The backbone of the tree.
Sibling	Two people share both parents.	Gives you a pair that must have the same two parents.
Marriage/Union	The two people who are parents of a child.	Determines who can be a parent for whom.
Gender	Often needed because “father” vs “mother”.	Helps filter impossible combinations.
Transitivity	If A is B’s parent and B is C’s parent, then A is C’s grandparent.	Allows you to deduce longer chains.
Exclusion	Two people cannot be both a parent and a child of the same person.	Rules out impossible loops.
Acyclicity	Family trees cannot contain cycles (A→B→C→A).	Avoids contradictions.

3. Common Strategy (Step‑by‑Step)

List all people and note their gender.
Write every clue in your own words.
Create a table (or diagram) with rows = parents, columns = children.
Mark definite entries (e.g., “A → B = yes”).
Use elimination – if person X is already a parent of Y, they cannot be a sibling with Y.
Apply transitivity to fill in grandparent/grandchild slots.
Check for contradictions – if a rule is violated, backtrack.
Resolve remaining blanks with the only possible choice left.
Double‑check all clues are satisfied.

4. Worked Example

Clues

A is the father of B.
C is the mother of D.
B and D are married.
E is the sibling of C.
F is the father of A.
G is the mother of E.

Goal: Draw the family tree and list all parent–child pairs.

Step 1 – List & Gender

Person	Gender
A	Male
B	Male
C	Female
D	Male
E	Male
F	Male
G	Female

Step 2 – Write Clues in Single‑Line Form

A → B (parent)
C → D (parent)
B ↔ D (married)
E ↔ C (siblings)
F → A (parent)
G → E (parent)

Step 3 – Build Parent–Child Table

Parent	Child
A	B
C	D
F	A
G	E

Step 4 – Resolve Sibling & Marriage Constraints

B ↔ D → They are married → They cannot share a parent.
→ B is not a child of C, nor D a child of A.
E ↔ C → Siblings → They must share the same parents F and G.
→ E is a child of F and G.

Step 5 – Final Tree

          F (Male) ──┐
                    │
          G (Female)┘
                    │
                ┌────┴────┐
                │         │
              A (Male)   E (Male)
              │
            ┌─┴─┐
            │   │
           B (Male)  (married to D)
                          │
                       C (Female)
                          │
                        D (Male)

All relationships satisfied?

A → B ✔️
C → D ✔️
B married D ✔️
E sibling C ✔️ (both children of F & G) ✔️
F → A ✔️
G → E ✔️

Yes!

5. Quick Revision Summary

#	Focus	Tip
1	Identify all people & genders	Write a quick table.
2	Translate every clue	Put “→”, “↔”, “married” in your own words.
3	Parent–child matrix	Mark definite entries; use “X” for impossible.
4	Sibling rule	Two people must share exactly the same parents.
5	Marriage rule	Married pair cannot be parent/child of each other.
6	Transitivity	A → B and B → C ⇒ A → C (grandparent).
7	No cycles	Check that no person is both ancestor and descendant.
8	Double‑check all clues	A single unsatisfied clue means a mistake.
9	Practice	Try at least 5 new puzzles per week.

Final Thought

Blood‑relation puzzles are all about systematic elimination and consistent bookkeeping. Once you set up a clear table or diagram, the logic flows naturally. Keep practicing with varied clue sets—soon the “aha!” moment will happen automatically. Happy solving!