π§ BRAIN-TEASER 11
Boatmen, Animal Weights & Finger Counting
TASK 01
π€ Two boatmen start simultaneously from opposite shores of a river and cross each other after 45 minutes from starting.
They row till they reach the opposite shore and return immediately. When will they cross each other again?
✅ Answer: 135 minutes (2 hours 15 minutes from start)
π Step-by-Step Explanation
First meeting after 45 minutes.
After meeting, both continue to opposite shores and turn back. They will meet again after covering additional distance.
Key insight: Between first and second meeting, together they cover twice the river width. Combined speed is constant.
Time from first meeting to second meeting = 2 × 45 = 90 minutes.
Total time from start = 45 + 90 = 135 minutes (2 hours 15 minutes).
π‘ Alternative explanation: They meet at the center first. Then each goes to opposite shore (45 min each) and meets again on return journey.
After meeting, both continue to opposite shores and turn back. They will meet again after covering additional distance.
Key insight: Between first and second meeting, together they cover twice the river width. Combined speed is constant.
Time from first meeting to second meeting = 2 × 45 = 90 minutes.
Total time from start = 45 + 90 = 135 minutes (2 hours 15 minutes).
π‘ Alternative explanation: They meet at the center first. Then each goes to opposite shore (45 min each) and meets again on return journey.
TASK 02
π» What is the weight of each animal? π¦π°
π» + π» = 120 kg
π° + π» = 70 kg
π» + π¦ + π° = 90 kg
π» Bear = 60 kg | π¦ Fox = 20 kg | π° Rabbit = 10 kg
Step-by-step solution:
• Bear + Bear = 120 → 2 Bears = 120 → Bear = 60 kg
• Rabbit + Bear = 70 → Rabbit + 60 = 70 → Rabbit = 10 kg
• Bear + Fox + Rabbit = 90 → 60 + Fox + 10 = 90 → Fox + 70 = 90 → Fox = 20 kg
π‘ This is a system of simple equations - a great introduction to algebra!
• Bear + Bear = 120 → 2 Bears = 120 → Bear = 60 kg
• Rabbit + Bear = 70 → Rabbit + 60 = 70 → Rabbit = 10 kg
• Bear + Fox + Rabbit = 90 → 60 + Fox + 10 = 90 → Fox + 70 = 90 → Fox = 20 kg
π‘ This is a system of simple equations - a great introduction to algebra!
TASK 03
"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!
We wonder how many birds of each kind
Aren't you going to help us find?"
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!
We wonder how many birds of each kind
Aren't you going to help us find?"
π¦ Parrots: 26 | π¦⬛ Crows: 52 | π¦ Sparrows: 104
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.
π‘ This charming poem-puzzle teaches ratios in a memorable way!
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.
π‘ This charming poem-puzzle teaches ratios in a memorable way!
TASK 04
π️ A young girl counted on her left hand fingers: Thumb=1, Index=2, Middle=3, Ring=4, Little=5,
then reverse: Ring=6, Middle=7, Index=8, Thumb=9, then Index=10, Middle=11, Ring=12, Little=13,
Ring=14, and so on. Which finger will be counted as 1000?
✅ Answer: INDEX FINGER
π Step-by-Step Explanation
The pattern repeats every 8 counts after the initial sequence.
Let's analyze the finger positions:
1: Thumb, 2: Index, 3: Middle, 4: Ring, 5: Little, 6: Ring, 7: Middle, 8: Index, 9: Thumb, 10: Index, 11: Middle, 12: Ring, 13: Little, 14: Ring, 15: Middle, 16: Index, 17: Thumb...
The cycle length is 8 (from 2 to 9, then 10 to 17, etc.).
For 1000: 1000 ÷ 8 = 125 remainder 0.
The remainder corresponds to position in cycle. After analysis, the 1000th count lands on the INDEX FINGER.
π‘ This puzzle demonstrates pattern recognition and modular arithmetic in a fun, real-world way!
Let's analyze the finger positions:
1: Thumb, 2: Index, 3: Middle, 4: Ring, 5: Little, 6: Ring, 7: Middle, 8: Index, 9: Thumb, 10: Index, 11: Middle, 12: Ring, 13: Little, 14: Ring, 15: Middle, 16: Index, 17: Thumb...
The cycle length is 8 (from 2 to 9, then 10 to 17, etc.).
For 1000: 1000 ÷ 8 = 125 remainder 0.
The remainder corresponds to position in cycle. After analysis, the 1000th count lands on the INDEX FINGER.
π‘ This puzzle demonstrates pattern recognition and modular arithmetic in a fun, real-world way!
π Why These Puzzles Matter π
• The boatmen puzzle teaches relative speed and combined distance concepts.
• Animal weight puzzles introduce systems of equations - the foundation of algebra.
• The birds poem makes ratios and proportions memorable and fun!
• Finger counting builds pattern recognition and modular arithmetic skills.
Mathematics is everywhere - from rivers to forests to your own fingers!
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All the best!
Thank You ππ»
All the best!
Thank You ππ»
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