EduCasheer × SiliconSpark — Classic Puzzles

Section A

Probability & Logic

Qismat A — Probability aur Mantiq

The Game Show Switch (Monty Hall Dilemma)

Game Show Switch — Monty Hall Masla

10 marks Probability Decision Theory ↗ Live Simulation

/ 10 marks

You are on a famous game show. There are 3 closed doors: one hides a luxury car, two hide goats. You pick Door 1. The host (who knows what's behind every door) opens Door 3 to reveal a goat, then offers you the chance to switch to Door 2.

Should you STICK with Door 1 or SWITCH to Door 2 to maximise your chance of winning the car?

(a)The probability if you stick vs. if you switch.
(b)Why it is NOT simply 50-50 after the host opens a door.
(c)A logical argument that convinces someone your choice is better.

Try It

🎰

Monty Hall Simulator

mathwarehouse.com

Urdu / Roman Hindi

Aap ek mashhoor game show mein hain. 3 band darwaze hain: ek ke peeche luxury car, do ke peeche bakri. Aap Door 1 chunte hain. Host Door 3 kholke bakri dikhata hai, phir Door 2 switch ka option deta hai.

Sawal: REHNA ya SWITCH karna chahiye?

Hint

Key insight: The host's action is not random — he always reveals a goat. This information changes the probabilities. Think about all possible scenarios from the start.

The Bomb Timer Water Puzzle (Die Hard Style)

Bomb Timer Paani Puzzle — Die Hard Style

10 marks Logic State Space ↗ Try Puzzle

/ 10 marks

You must place EXACTLY 4 liters on a scale to stop a bomb from exploding. You only have access to:

▸ A 5-liter jug (no markings)

▸ A 3-liter jug (no markings)

▸ A fountain with unlimited water

ALLOWED: fill completely · empty completely · pour one into other until full or empty

Describe the EXACT numbered step-by-step sequence to get exactly 4 liters in one jug. Explain briefly WHY your final step yields exactly 4 liters.

Try It

💧

Water Jug Puzzle

mathsisfun.com

Urdu / Roman Hindi

Scale par BILKUL 4 liter rakhne hain warna bomb phat jayega. Sirf 5-liter jug, 3-liter jug aur fountain hai. Bilkul numbered qadam ba qadam sequence batayein. Aakhir mein samjhaein ke 4 liter KYUN ban gaye.

Hint

Approach: Fill the 5L jug, pour into 3L until full. Empty the 3L. Pour the remaining 2L into the 3L. Fill 5L again... think about what 5 − 3 + 2 gives you.

Section B

Algorithmic Thinking

Qismat B — Algorithmic Soch

The Golden Disk Tower (Tower of Hanoi — 3 Disks)

Sunehri Diskon ka Minar — Tower of Hanoi

10 marks Recursion Algorithms ↗ Play Game

/ 10 marks

A · START

→

B · HELPER

→

C · GOAL

Three pillars: A, B, C. Pillar A has 3 disks (largest at bottom). Rules: move one disk at a time; never place a larger disk on a smaller one. Move the entire tower from A to C using B as helper.

Write the COMPLETE numbered move sequence. Then answer (a)–(d) below.

(a)Minimum moves needed for 3 disks?
(b)Minimum moves for 4 disks?
(c)General formula for n disks?
(d)Briefly explain the recursive logic of your solution.

Try It

🗼

Tower of Hanoi Game

mathsisfun.com

Urdu / Roman Hindi

Teen pillars: A, B, C. Pillar A par 3 disks hain (bara neeche). Ek waqt ek disk; kabhi bara disk chhote par na rakhein. Poora minar A se C par le jao, B helper hai. POORI numbered moves sequence likhein.

Hint

Recursive insight: To move n disks to C, first move n−1 disks to B, then move the largest to C, then move n−1 disks from B to C.

The Five Philosophers' Eternal Feast (Dining Philosophers)

Paanch Falsafa-daanon ki Abdi Daawat

10 marks Concurrency OS Theory Deadlock

/ 10 marks

5 philosophers sit at a round table. Each needs 2 chopsticks to eat, but only 5 chopsticks exist (one between each pair). If all grab their left chopstick simultaneously — DEADLOCK, nobody eats forever.

Design a fair protocol/strategy so that no philosopher starves AND deadlock is impossible.

(a)No philosopher ever starves (everyone eats infinitely often). Koi falsafa-daan kabhi bhooka na mare.
(b)Deadlock is impossible. Deadlock kabhi na ho.

Clearly state your rules and explain WHY they prevent both deadlock and starvation.

Urdu / Roman Hindi

5 falsafa-daan gol mez par baithe hain. Har ek ko 2 chopsticks chahiye, lekin sirf 5 hain. Ek aisa fair protocol/strategy banayein ke koi bhooka na mare aur deadlock kabhi na ho. Apne qanoon saaf batayein.

Key Concepts

Deadlock — circular wait where no one can proceed.

Starvation — one thread never gets CPU/resource time.

Think about: Asymmetry, Resource hierarchy, or a waiter/arbitrator solution.

Section C

Mathematical Paradoxes

Qismat C — Mathemati ke Ajeeb Maslay

The Faulty Algebraic Proof — 2 = 1

Ghalat Algebric Sabit — '2 = 1'

10 marks Algebra ⚠ Find the Error

/ 10 marks

A student 'proves' 2 = 1 using the steps below (given: a = b, a ≠ 0). One step contains a critical mathematical error. Your job is to find it.

Step 1	a = b	Given
Step 2	a² = ab	× a both sides
Step 3	a² − b² = ab − b²	− b² both sides
Step 4	(a−b)(a+b) = b(a−b)	Factorise
Step 5	a + b = b	÷ (a−b) ← ??
Step 6	2b = b	Since a = b
Step 7	2 = 1	÷ b both sides

①Identify EXACTLY which step first contains the error. Quote the incorrect line.
②Explain which algebra rule is violated and why.
★(Bonus) Why do many people miss this mistake at first glance?

Urdu / Roman Hindi

Ek talib-e-ilm 2 = 1 'sabit' karta hai. BILKUL woh step batayein jahan pehli ghalti hai. Ghalat line quote karein. Algebra ka kaun sa qanoon toota aur kyun? (Bonus) Log pehli nazar mein ghalti kyun miss kar dete hain?

Hint

Think about: What is the value of (a − b) when a = b? Is it legal to divide both sides of an equation by this expression? What rule in mathematics governs division?

The Missing Rupee Mystery

Gayab Rupaye ka Raaz

10 marks Accounting Paradox Logic

/ 10 marks

3 friends pay ₹30 for a hotel room (₹10 each). The manager later decides to refund ₹5 via a bellboy. The dishonest bellboy pockets ₹2 and gives ₹1 back to each friend.

Person	Paid	Got Back	Net Paid
Each friend (×3)	₹10	₹1	₹9
Bellboy kept	—	—	₹2
Misleading total?			₹27 + ₹2 = ₹29??

"Where is the missing ₹1 from the original ₹30?"

(a)Why the equation "₹27 + ₹2 = ₹29" is mathematically correct but logically misleading.
(b)Show the CORRECT accounting of all ₹30 so nothing is missing.

Urdu / Roman Hindi

3 dost hotel room ke liye ₹30 dete hain. Manager ₹5 wapas karta hai ek bure bellboy ke zariye jo ₹2 khud rakhta hai aur ₹1 har dost ko deta hai. Log poochte hain: ₹30 mein se ek rupaya kahan gaya? Saaf hisaab dikhao.

Hint

The trick: The puzzle adds ₹27 + ₹2 but these numbers already overlap! The ₹2 is part of the ₹27, not something separate. Ask: what should you add to ₹27 to reach ₹30?