By signing in you confirm you are 18 or older, or have your parent’s or guardian’s consent.

UPSC Prelims 2026 CSAT, question 15

Topic: Counting and probability

Q15

The top of a table is rectangular and its dimensions are 6′×10′6' \times 10'. Two rectangular portions of the table top are painted in blue colour; both these portions have dimensions 2.5′×8′2.5' \times 8' and each of them has exactly two sides common with two edges of the table top. If the table is fixed to the ground and the remaining portion of the table top is painted in white, how many different patterns are possible when observed from above?

  1. (a) 2
  2. (b) 4Correct answer
  3. (c) 6
  4. (d) 8

Solution.

Answer: (b) 4

  1. Each 2.5′×8′2.5' \times 8' blue rectangle has two sides common with two edges of the 6′×10′6' \times 10' table, so each must fit into a corner with its 8′8' side along a 10′10' edge and its 2.5′2.5' side along a 6′6' edge.
  2. Two disjoint 2.5′×8′2.5' \times 8' corner rectangles cannot share the same 10′10' edge (since 8′+8′=16′>10′8' + 8' = 16' > 10'), so one lies along one 10′10' edge (2 corner choices) and the other along the opposite 10′10' edge (2 corner choices).
  3. Because the table is fixed to the ground, all orientations are distinct, giving 2×2=42 \times 2 = 4 possible patterns.

Trap: If the two 2.5′×8′2.5' \times 8' blue rectangles are permitted to overlap along the same 10′10' edge, any 2 of the 4 corners can be chosen in (42)=6\binom{4}{2} = 6 ways, which is option (c).