Grids mein Khoj

Class 7 Maths · Chapter 6: Number Play · NCERT Ganita Prakash section 6.3

Seekho

3 × 3 grid ko 1 se 9 se bharo, har ek ek baar, aur har pankti aur stambh ka jod bahar likho. Zoya dekhti hai: teeno pankti-jod hamesha 45 jodte hain, aur teeno stambh-jod bhi. Kyun? Panktiyan milkar har number ek baar rakhti hain: 1 + 2 + … + 9 = 45.

1 + 2 + … + 9 = 45

Kuch paheliyan asambhav hain: 1–9 ke teen alag numbers ki pankti kam se kam 1 + 2 + 3 = 6 aur zyaada se zyaada 7 + 8 + 9 = 24. 5 ya 26 pankti-jod maangne wala grid kabhi nahi bharega.

6 ≤ row sum ≤ 24

Magic square mein har pankti, stambh aur vikarn ka jod ek hi magic sum hota hai. 1–9 mein panktiyan kul 45, to har pankti 45 ÷ 3 = 15. Beech mein 5 hona chahiye (9 ho to 8 + 9 pehle hi bada; 1 ho to 2 + 1 ko 12 chahiye). Aur 1 aur 9 kone mein nahi baith sakte.

8 1 6 / 3 5 7 / 4 9 2

Aam roop: beech mein m ho to lagaataar numbers ka magic square: m + 3, m − 4, m + 1 / m − 2, m, m + 2 / m − 1, m + 4, m − 3. Har line ka jod 3m. Har khaane mein ek hi number jodo ya har khaane ko ek hi number se guna karo, phir bhi magic. Khajuraho ka 10vi sadi ka Chautīsā Yantra 4 × 4 magic square hai, jod 34.

each line = 3m

Explore: magic numbers.

1. 1–9 se bane magic square ka magic sum set karo.
2. Beech mein jo number hona chahiye, wo set karo.
3. Magic square ke beech mein 25 hai. Magic sum set karo.

Yaad rakho

• 1–9 ke 3 × 3 grid mein pankti-jod (aur stambh-jod) milkar 45.
• 1–9 magic square ka jod 15 aur beech mein 5; aam taur par har line = 3 × beech.

Quick check

Magic square 11 se 19 use karta hai. Beech mein kya?

1. 15
2. 11
3. 45
4. 19

Socho

Aisa magic square banao jiska magic sum 60 ho.

Practice

Teen levels (easy, medium, hard) ke naye sawaalon se practice karo, kuch hands-on, hints aur hal ke saath. Topic poora karne ke liye pichhle 5 mein se 4 sahi karo.