🎙 Introduction / परिचय
Figure Counting में किसी diagram में hidden lines, triangles, squares, rectangles आदि की संख्या गिनी जाती है।
Delhi Police में केवल basic triangle‑counting, square‑counting और line‑counting आते हैं।
✔ Solved Examples (Delhi Police Pattern)
Example 1 – Basic Triangle Count:
If a triangle is divided into 4 smaller triangles (top, left, right, bottom):
Small = 4
Large (whole) = 1
Total = 5 triangles
Example 2 – Square Count:
2×2 grid:
Small squares = 4
Big square = 1
Total = 5 squares
Example 3 – Rectangle Count:
2×3 grid:
Rectangles = m(m+1) × n(n+1) / 4
= 2×3 grid → 2×3 gives 18 rectangles
Ans = 18
Example 4 – Lines Count:
If 3 parallel lines intersect 2 other parallel lines:
Intersections = 3×2 = 6
Total segments = 6×2 = 12
Example 5 – Complex Triangle (simple DP level):
A triangle cut by 1 horizontal and 1 vertical line:
Total triangles ≈ 6
Ans = 6
🔥 Challenge Question
How many triangles are there in the diagram of a triangle with 3 horizontal partitions?
Using formula for layered triangle: n(n+2)(2n+1)/8 for n=3
= 3×5×7 / 8 = 105/8 ≈ 13 triangles