Puzzles

🚀 Study Notes – “Puzzles”

Reasoning Ability – Nagaland Patwari / Lekhpal Program

1. What are Puzzles?

• Puzzles are little brain‑games that use a set of rules or facts to find an answer.
• Think of them as a story with clues that you need to solve.
• They help you practice observation, logic, and creativity.

2. Everyday Analogy

• Imagine you’re a detective in a grocery shop:
  • Clues are the prices, colours, and sizes of items.
  • Goal is to find out which item is the cheapest.
  • You use the clues to rule out possibilities until only one item fits.

3. Types of Puzzles You’ll See

4. Simple Strategy for Every Puzzle

1. Read the whole puzzle once.
   Don’t jump straight to answering.
2. Write down the facts – use a small table or list.
   Every clue is a small piece of a bigger picture.
3. Look for “must‑be” facts.
   If something is said to be “first”, it is the earliest.
4. Eliminate impossible options.
   If one clue says “A is not next to B”, then that placement is gone.
5. Fill in the blanks step by step.
   Often one clue will let you place one item, then another clue will use that placement to place the next.
6. Check your answer – make sure every clue is satisfied.

Remember:
Every puzzle is just a chain of small “yes/no” tests.
If you can answer “yes” or “no” to each clue and still satisfy all, you’re done!

5. Tiny Example – Ordering Puzzle

Problem
Three friends – A, B, and C – are standing in a line from left to right.

• A is not at the rightmost position.
• B is to the left of C.

Question: Who is in the middle?

Solution

1. List possibilities

   • Left – Middle – Right
   • Possible orders:
     1. A B C
     2. A C B
     3. B A C
     4. B C A
     5. C A B
     6. C B A

2. Apply clue 1 (A not rightmost)

   • Remove any order where A is on the right:
     • A C B (A is left, ok)
     • A B C (A is left, ok)
     • B A C (A is middle, ok)
     • B C A (A is right, ❌)
     • C A B (A is middle, ok)
     • C B A (A is right, ❌)

   Remaining: 1, 2, 3, 5

3. Apply clue 2 (B left of C)

   • Check each remaining order:
     • A B C → B left of C ✔
     • A C B → B right of C ❌
     • B A C → B left of C ✔
     • C A B → B right of C ❌

   Remaining: 1 and 3

4. See who is middle

   • Order 1: A B C → B is middle.
   • Order 3: B A C → A is middle.

   Both satisfy all clues – but we need a unique answer.
   Re‑read clues: “B is to the left of C.” In order 3, B is left of C, yes.
   But check clue 1 again: “A is not at the rightmost position.” In order 3, A is middle – still okay.

   We have two possible solutions → Did we miss something?
   Actually, the puzzle as written has two correct answers – that’s fine for practice.
   Answer: B can be middle or A can be middle, depending on arrangement.

Lesson:

• Write down all possibilities first.
• Narrow down step by step.
• If you end with more than one answer, double‑check the clues.

6. Quick Tips

• Use a small table – columns for each position, rows for each person/item.
• Colour‑code: pick a colour for each person; stick it to the table.
• Keep it short: write only what you’re sure of; don’t crowd the note.
• Practice: solve 5 puzzles every day; you’ll get faster!

7. Sample Practice Problems

1. Sequence – What comes next?
   2, 4, 8, 16, ___

2. Ordering – Four houses are in a row:

   • The blue house is on the left of the green house.
   • The red house is right of the yellow house.
   • The green house is next to the blue house.
     Who lives in the middle house?

3. Pattern – Identify the missing