Скачать или смотреть Number Play Q.5|Page122|Class8 Maths NCERT|Chapter 5|Ganita Prakash.I hold some pebbles not too many

Welcome to Ganita Prakash – The Territory of Mathematics!
In this video, we’ll solve a fun riddle-type question from Class 8 Maths Chapter 5: Number Play (NCERT 2025) —

📘 Question:
“I hold some pebbles, not too many, When I group them in 3’s, one stays with me. Try pairing them up — it simply won’t do, A stubborn odd pebble remains in my view. Group them by 5, yet one’s still around, But grouping by seven, perfection is found. More than one hundred would be far too bold, Can you tell me the number of pebbles I hold?”

🧩 What You’ll Learn
✅ Representing number riddles using algebra and remainders
✅ Finding numbers satisfying multiple remainder conditions
✅ Applying divisibility concepts in real-world riddles
✅ Using logic to check number conditions step-by-step

🧮 Step-by-Step Solution
Let the number of pebbles be x.
x leaves remainder 1 when divided by 2 → x = 2a + 1
x leaves remainder 1 when divided by 3 → x = 3b + 1
x leaves remainder 1 when divided by 5 → x = 5c + 1
x is divisible by 7 → x = 7k

So, x satisfies x ≡ 1 (mod 2), x ≡ 1 (mod 3), x ≡ 1 (mod 5), and x ≡ 0 (mod 7).
The least common multiple of 2, 3, and 5 is 30.
So numbers that give remainder 1 for all are of the form 30m + 1.
Now x must also be divisible by 7 → 30m + 1 = 7n.
Checking values of m: for m = 2 → 30×2 + 1 = 61 (not multiple of 7), m = 4 → 121 (not multiple), m = 5 → 151 (not multiple), m = 6 → 181 (not multiple), m = 3 → 91 ✅ divisible by 7.
✅ Therefore, x = 91.

💡 Concept Recap
We used remainders and modular arithmetic to find a number fitting several divisibility patterns.
This strengthens understanding of the Chinese Remainder Theorem conceptually, showing how patterns repeat across multiples.

📘 Book & Chapter Info
📗 Book: NCERT Mathematics
📘 Chapter: Number Play
📖 Page: 126
🎯 Class: 8 (CBSE / NCERT 2025)
📚 Topic: Number Riddles with Remainders

🎯 Why Watch This Video?
⭐ Solving logical riddles with algebra
⭐ NCERT-based fun maths problem
⭐ Connects reasoning, divisibility, and logic
⭐ Builds number sense for competitions and exams

💬 Who Should Watch
👩‍🏫 Class 8 CBSE Students
👨‍🎓 NCERT Learners
📘 Teachers & Tutors
👨‍👩‍👧 Parents Helping Kids

🔔 Don’t Forget
✅ Like 👍
✅ Comment 💬
✅ Subscribe 🔔
✅ Share with friends to help them learn too!

🧠 Extra Practice Ideas
Try changing “divisible by 7” to “divisible by 6” and find new results.
Make your own riddles with remainders and check solutions using algebra.

📚 Watch More Videos
🎥 Class 8 Maths Chapter 5 – Number Play Full Chapter Explanation
🎥 Class 8 Maths – Divisibility Tricks
🎥 Number Play – Remainder Logic Explained
🎥 Maths Riddles and Patterns – CBSE Class 8

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