Figure Counting: SSC CGL Reasoning

Formulas (1)

• Labelling points and listing triangles · Triangles from lines through one corner
  $$\text{triangles} = \frac{k(k+1)}{2}$$

Watch out for (4)

• Counting only the smallest triangles
  → Labelling points and listing triangles
• Counting three points that lie on one line
  → Labelling points and listing triangles
• Adding the blocks and stopping
  → Counting a large figure block by block
• Counting a shared triangle in both blocks
  → Counting a large figure block by block

Formulas (2)

• Squares in grids and overlapping squares · Squares in an n by n grid
  $$1^2 + 2^2 + \cdots + n^2 = \frac{n(n+1)(2n+1)}{6}$$
• Rectangles, circles and semicircles · Rectangles in a grid
  $$\binom{m+1}{2} \times \binom{n+1}{2}$$

Watch out for (4)

• Counting only the single cells
  → Squares in grids and overlapping squares
• Using the n by n rule on a grid that is not square
  → Squares in grids and overlapping squares
• Forgetting that a square is a rectangle
  → Rectangles, circles and semicircles
• Closing an open figure in your head
  → Rectangles, circles and semicircles