The top of a table is rectangular and its dimensions are 6′ × 10′. Two rectangular portions of the table top are painted in blue colour; both these portions have dimensions 2.5′ × 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?

Why the correct option is correct: To form the pattern, two 2.5' × 8' blue rectangular portions must be placed on a 6' × 10' table. Because each blue portion shares exactly two sides with the table's edges, they must be situated in the corners. The 8' length of the blue rectangle cannot fit along the 6' width of the table, so it must align with the 10' length, while the 2.5' side aligns with the 6' width. This leaves 4 fixed corner positions for the blue rectangles.

Choosing 2 corners out of 4 provides ⁽⁴₂⁾ = 6 possible pairs. However, we must consider spatial overlap. If two blue rectangles are placed on the same 10' edge, their combined length (8' + 8' = 16') exceeds the table's 10' boundary. They would overlap, merging into a single non-rectangular shape (or a single fused rectangle) and violating the condition of having "two rectangular portions." Subtracting these 2 overlapping pairs (top edge and bottom edge) leaves 6 - 2 = 4 valid combinations: two pairs sharing a 6' edge (where the combined width is 2.5' + 2.5' = 5' ≤ 6', meaning no overlap) and two diagonal pairs. With the table fixed to the ground, these 4 configurations yield distinct patterns.

Why the wrong options are wrong:

• Option A (2): Fails to count the non-overlapping adjacent pairs sharing the 6' edges, only counting the diagonals.
• Option C (6): Fails to account for the spatial overlap constraint along the 10' edges, improperly including the merged shapes.
• Option D (8): Incorrectly assumes the 8' side can be placed along the 6' edge, or miscalculates the available spatial orientations.

Takeaway: In spatial reasoning problems, combinatorics formulas like ⁽⁴₂⁾ must be cross-checked against physical boundaries. Overlap constraints frequently eliminate theoretical combinations.