Question:
Find the number of squares in an 8×8 chessboard.
एक 8×8 शतरंज की बिसात में वर्गों की कुल संख्या ज्ञात कीजिए।
Options:
- 204
- 64
- 128
- 256
- 204
- 64
- 128
- 256
Correct Answer: a)
Explanation:
Total squares in an \(n \times n\) grid = \(\sum_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}{6}\).
For \(n = 8\): \(\frac{8 \times 9 \times 17}{6} = 4 \times 3 \times 17 = 204\).
For \(n = 8\): \(\frac{8 \times 9 \times 17}{6} = 4 \times 3 \times 17 = 204\).
\(n \times n\) ग्रिड में वर्गों की संख्या = \(\frac{n(n+1)(2n+1)}{6} = \frac{8 \times 9 \times 17}{6} = 204\)।