Brain Teasers 04

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🧠 BRAIN-TEASER 04
Remainders, Water Jugs & Auditorium

🔢 Remainder Patterns: (a) 9 and 16 remainders? (b) 12 and 14 remainders?

✅ Answer: See below

9,16: 9,2,11,4,13,6,15,8,1,10,3,12,5,14,7 (all 1-15)

12,14: 12,10,8,6,4,2,0,12,10,8,6,4,2 (only evens)

📖 Explanation: When gcd(m,n)=1, remainders cover all numbers. gcd(12,14)=2 → only multiples of 2 appear.

💧 Water Jug Puzzle: 9L and 5L cans. Get 3L. Bonus: 8L and 6L → get 5L?

✅ Answer: 3L possible. 5L from (8,6) impossible

📖 Method: Fill 9L→pour to 5L→4L left. Empty 5L, pour 4L. Fill 9L→pour to 5L (needs 1L)→8L left. Empty 5L, pour 8L→3L left. Bonus: gcd(8,6)=2 → only multiples of 2 possible, not 5.

🏛️ Auditorium: East wall 108m², north wall 135m², floor 180m². Find height.

✅ Answer: 9 metres

📖 Explanation: B×H=108, L×H=135, L×B=180. Multiply: (LBH)²=108×135×180=2,624,400 → LBH=1620 → H=1620/180=9.

🔁 Two-digit number: subtract 4 from units, add 4 to tens → double the original. Find number.

✅ Answer: 36

📖 Explanation: Original=10a+b. New=10(a+4)+(b-4)=10a+b+36. Given 10a+b+36=2(10a+b) → 36=10a+b → number=36.

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