BRAIN-TEASERS 08

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🧠 BRAIN-TEASER 08
Riddles, Birds, Coins, Vats & Painted Cube

🔢 Number Riddle (i): "Take away from me the number eight, Divide further by a dozen to come up with a full team for a game of cricket!" Find the number.

✅ Answer: 140

📐 Solution

A cricket team has 11 players. Working backwards: Let the number be N.
(N - 8) ÷ 12 = 11 → N - 8 = 132 → N = 140.
Check: 140 - 8 = 132, 132 ÷ 12 = 11 ✓

🔢 Number Riddle (ii): "Add four to six times a number, To get exactly sixty four!" Find the number.

✅ Answer: 10

📐 Solution

Let the number be x. Equation: 6x + 4 = 64 → 6x = 60 → x = 10.
Check: 6×10 + 4 = 60 + 4 = 64 ✓

🐦 Birds on the Peepal Tree

There was in the forest an old Peepal tree
The grand tree had branches ten and three
On each branch there lived birds fourteen
Sparrows brown, crows black and parrots green!
Twice as many as the parrots were the crows
And twice as many as the crows were the sparrows!

🐦 Answer: Sparrows: 104, Crows: 52, Parrots: 26

Step-by-step solution:
Total branches = 13, birds per branch = 14 → Total birds = 13 × 14 = 182.
Let parrots = p, crows = 2p, sparrows = 2 × (2p) = 4p.
Total: p + 2p + 4p = 7p = 182 → p = 26.
Parrots = 26, Crows = 52, Sparrows = 104.
💡 This charming poem-puzzle teaches ratio and proportion in a fun way!

💰 Five-Rupee and Two-Rupee Coins

Problem: The number of two-rupee coins is twice the number of five-rupee coins. Total money is ₹108. How many of each coin?

💰 Answer: Five-rupee coins: 12, Two-rupee coins: 24

Step-by-step solution:
Let number of five-rupee coins = x. Then two-rupee coins = 2x.
Total value: 5x + 2(2x) = 5x + 4x = 9x = 108 → x = 12.
Five-rupee coins = 12, Two-rupee coins = 24.
Check: 12×5 = 60, 24×2 = 48, Total = ₹108 ✓

📦 Things in Vats (Nested Counting)

Problem: 2 vats, each containing 2 mats. 2 cats sat on each mat. Each cat wore 2 funny old hats. On each hat lay 2 thin rats. On each rat perched 2 black bats. How many things in total?

🐱 Answer: 124 things

Step-by-step multiplication:
Vats: 2
Mats: 2 vats × 2 mats = 4 mats
Cats: 4 mats × 2 cats = 8 cats
Hats: 8 cats × 2 hats = 16 hats
Rats: 16 hats × 2 rats = 32 rats
Bats: 32 rats × 2 bats = 64 bats
Total things = 2 + 4 + 8 + 16 + 32 + 64 = 124
💡 This is a great lesson in repeated multiplication and geometric progression!

🧊 Painted Cube Puzzle

Problem: 27 small cubes are glued to make a big cube (3×3×3). The exterior is painted yellow. How many small cubes have paint on:

🎨 (i) Only one face: 6 | (ii) Two faces: 12 | (iii) Three faces: 8

Explanation:
• 3×3×3 cube has 27 small cubes.
• Corner cubes (8) have 3 faces painted.
• Edge cubes but not corners: each edge has 1 middle cube × 12 edges = 12 cubes with 2 faces painted.
• Face centers (not edges): each face has 1 center cube × 6 faces = 6 cubes with 1 face painted.
• Interior cubes (1) have no paint. Check: 8 + 12 + 6 + 1 = 27 ✓
💡 This is a classic spatial visualization problem!

🌟 Why These Puzzles Matter 🌟

• Number riddles build equation-solving skills.
• The birds poem teaches ratios in a memorable way.
• Coin problems apply algebra to real-life money.
• Nested counting develops systematic thinking.
• The painted cube builds 3D visualization skills.

Mathematics is everywhere — in riddles, poems, coins, and cubes!

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