TANCET MCA Figure Counting Previous Year Questions (PYQs)
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Find the number of triangles in the given
figure.
1
2
3
4
Solution
Step-wise counting (short):
Small triangles inside star → 10
Medium triangles (combining small ones) → 8
Larger triangles across structure → 6
Biggest triangles → 2
Total:
10+8+6+2=26
Find the minimum number of straight
lines required to make the given figure. 
1
2
3
4
Solution
Minimum number of straight lines required = 16.
Counting line-wise:
Horizontal lines = 3
Top horizontal = 1, middle horizontal = 1, bottom horizontal = 1
Vertical lines = 4
Left side = 1, right side = 1, two inner verticals = 2
Slant lines = 9
Left upper outer slant = 1
Left upper inner slant = 1
Right upper inner slant = 1
Right upper outer slant = 1
Left lower outer slant = 1
Left lower inner slant = 1
Right lower inner slant = 1
Right lower outer slant = 1
Middle top-to-bottom slant/straight connection counted = 1
Total = 3 + 4 + 9 = 16
Hence, the minimum number of straight lines is 16. Final Answer: (a) 16
Counting line-wise:
Horizontal lines = 3
Top horizontal = 1, middle horizontal = 1, bottom horizontal = 1
Vertical lines = 4
Left side = 1, right side = 1, two inner verticals = 2
Slant lines = 9
Left upper outer slant = 1
Left upper inner slant = 1
Right upper inner slant = 1
Right upper outer slant = 1
Left lower outer slant = 1
Left lower inner slant = 1
Right lower inner slant = 1
Right lower outer slant = 1
Middle top-to-bottom slant/straight connection counted = 1
Total = 3 + 4 + 9 = 16
Hence, the minimum number of straight lines is 16. Final Answer: (a) 16
The square boxes in the figures given are
to be painted with different colours such
that no two adjacent boxes (even
diagonally) have same colour. How many
minimum colours do you need in each
case?
1
2
3
4
Solution
Condition: No two adjacent boxes (including diagonally) can have the same colour.
First Figure (cross shape):
Due to diagonal touching, 3 colours are not sufficient.
Minimum colours required = 4
Second Figure (3×3 grid):
Each box touches many others including diagonally, forming a highly connected pattern.
At least 4 colours are required to avoid repetition.
Final Answer: (b) (4, 4)
First Figure (cross shape):
Due to diagonal touching, 3 colours are not sufficient.
Minimum colours required = 4
Second Figure (3×3 grid):
Each box touches many others including diagonally, forming a highly connected pattern.
At least 4 colours are required to avoid repetition.
Final Answer: (b) (4, 4)
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