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?

• The table is a 6' × 10' rectangle. The blue portions are 2.5' × 8' rectangles, each sharing exactly two sides with the table edges, meaning they must be placed in the corners.

• For a 2.5' × 8' rectangle to fit in a corner of a 6' × 10' table, the 8' side must align with the 10' side of the table, and the 2.5' side must align with the 6' side. This is because 8' < 10' and 2.5' < 6', but 8' > 6' and 2.5' < 10' would not allow the 'two sides common' condition to be met with the specific dimensions relative to the table's orientation if rotated incorrectly (specifically, the 8' side cannot align with the 6' side of the table as 8 > 6). Thus, the blue rectangles are fixed in orientation relative to the table's long axis.

• There are 4 corners on the table. Each blue rectangle can be placed in any of the 4 corners.

• Since the two blue portions are identical and distinct from the white portion, we are choosing 2 distinct corners out of 4 for the blue rectangles. The number of ways to choose 2 corners from 4 is C(4,2) = 6.

• However, the question asks for 'different patterns' observed from above. We must consider rotational symmetry. The table is rectangular (6x10), not square, so it has only 180-degree rotational symmetry (and reflectional symmetry if we consider the table itself, but 'patterns' usually imply distinct visual arrangements). Let's re-evaluate based on distinct visual patterns.

• Actually, let's look at the positions. The corners are Top-Left (TL), Top-Right (TR), Bottom-Left (BL), Bottom-Right (BR). The blue rectangles are 2.5x8. The 8' side is along the 10' edge. So the blue rectangle occupies 8' of the 10' length and 2.5' of the 6' width.

• Let's list the pairs of corners: (TL, TR), (TL, BL), (TL, BR), (TR, BL), (TR, BR), (BL, BR).

• Due to the 180-degree rotational symmetry of the rectangle, (TL, BR) is equivalent to (TR, BL) if we rotate the table 180 degrees? No, TL and BR are opposite. TR and BL are opposite. Rotating 180 degrees maps TL to BR and TR to BL. So the pattern with blue at TL and BR is the same as the pattern with blue at BR and TL (which is the same set). The pattern with blue at TR and BL is the same as the pattern with blue at BL and TR. Are (TL, BR) and (TR, BL) distinct? Yes, one has blue on the main diagonal, the other on the anti-diagonal. But wait, if you rotate the table 180 degrees, the 'Top' becomes 'Bottom'. The pattern with blue at TL and BR looks identical to the pattern with blue at BR and TL. The pattern with blue at TR and BL looks identical to the pattern with blue at BL and TR. Are these two patterns distinct from each other? Yes. One has blue corners touching the 'top' and 'bottom' edges at the same horizontal ends? No. TL is (0,6) to (2.5, 8) if origin is bottom-left? Let's use coordinates. Table [0,10]x[0,6]. Blue is 8x2.5. It must be 8 along x, 2.5 along y. So it occupies x in [0,8] or [2,10] and y in [0,2.5] or [3.5,6].

• Corner 1 (Bottom-Left): x[0,8], y[0,2.5].

• Corner 2 (Bottom-Right): x[2,10], y[0,2.5].

• Corner 3 (Top-Left): x[0,8], y[3.5,6].

• Corner 4 (Top-Right): x[2,10], y[3.5,6].

• Possible pairs of corners:

1. BL & BR: Blue at bottom edge. White in middle and top. Pattern: Two blue blocks at bottom.

2. TL & TR: Blue at top edge. White in middle and bottom. This is the 180-degree rotation of Pattern 1. If the table is fixed to the ground, 'observed from above' usually implies a fixed orientation (e.g., North is up). If the table is fixed, Top is Top. So Pattern 1 (Blue at Bottom) is distinct from Pattern 2 (Blue at Top). Wait, the question says 'table is fixed to the ground'. This implies we cannot rotate the table to make patterns match. We observe it from above. So Top is distinct from Bottom. Left is distinct from Right? No, Left and Right are distinct positions. But is the pattern 'Blue at BL and BR' distinct from 'Blue at TL and TR'? Yes, one has blue at the bottom, one at the top.

3. BL & TL: Blue at Left edge. White at Right. Pattern: Blue on the left side.

4. BR & TR: Blue at Right edge. White at Left. Pattern: Blue on the right side. Distinct from 3.

5. BL & TR: Blue at Bottom-Left and Top-Right. Diagonal.

6. BR & TL: Blue at Bottom-Right and Top-Left. Anti-diagonal.

• Are 5 and 6 distinct? Yes. In 5, the blue blocks are at (0,0) and (10,6) roughly. In 6, they are at (10,0) and (0,6). Since the table is fixed, these are different visual patterns.

• So we have 6 distinct patterns: (BL,BR), (TL,TR), (BL,TL), (BR,TR), (BL,TR), (BR,TL).

• Therefore, there are 6 different patterns.