अशाब्दिक तर्क — Counting Figures र Spatial Intelligence
यस नोटमा triangles, squares, lines count गर्ने र 3D spatial reasoning सम्बन्धी प्रश्नहरूको अभ्यास गरिन्छ।
Counting Triangles
Formula
n रेखाले बनाएको triangle मा:
Total triangles = n(n+2)(2n+1)/8 (यदि n even)
Simple approach: छोटा triangles count + combination count
| Figure | Small △ | Medium | Large | Total |
|---|---|---|---|---|
| Basic △ (3 parts) | 3 | — | 1 | 4 |
| △ (4 parts) | 4 | 3 | 1 | 8 (approx) |
Counting Squares र Rectangles
Formula
m×n grid मा:
Squares = Σ (m−i+1)(n−i+1) for i=1 to min(m,n)
Rectangles = [m(m+1)/2] × [n(n+1)/2]
Example: 3×3 grid → Squares: 9+4+1 = 14
Figure Ground Perception
Complex figure भित्र simple target figure खोज्दा:
1. Target figure को sides/angles note गर्नुस्
2. Complex figure मा same proportional shape trace गर्नुस्
3. Rotation/reflection allowed हुन्छ (यदि प्रश्नले नभने)
3D Figures — Views
| View | नेपाली | हेर्ने तरिका |
|---|---|---|
| Front view | अगाडिबाट | X-Y plane |
| Side view | छेउबाट | Y-Z plane |
| Top view | माथिबाट | X-Z plane |
Quick Recall:
• 3×3 grid squares: 9+4+1 = 14
• 4×4 grid squares: 16+9+4+1 = 30
• m×n rectangles: [m(m+1)/2] × [n(n+1)/2]
• Target figure: sides count गर्नुस् → proportional trace गर्नुस्
• 3×3 grid squares: 9+4+1 = 14
• 4×4 grid squares: 16+9+4+1 = 30
• m×n rectangles: [m(m+1)/2] × [n(n+1)/2]
• Target figure: sides count गर्नुस् → proportional trace गर्नुस्
Q1. 4×4 grid मा कति squares छन्?
(A) 16 (B) 20 (C) 30 (D) 36
→ (C) 30 → 16+9+4+1=30
(A) 16 (B) 20 (C) 30 (D) 36
→ (C) 30 → 16+9+4+1=30