एक मेज़ का ऊपरी पृष्ठ (top of a table) आयताकार है और उसके आयाम 6' x 10' हैं। मेज़ के ऊपरी पृष्ठ के दो आयताकार भागों को नीले रंग से रंगा गया है; इन दोनों भागों के आयाम 2.5' x 8' हैं और उनमें से प्रत्येक की सटीक दो भुजाएँ, मेज़ के ऊपरी पृष्ठ के दो किनारों के उभयनिष्ठ हैं। यदि मेज़ को जमीन पर स्थिर रखा जाता है और मेज़ के ऊपरी पृष्ठ के शेष भाग को सफ़ेद रंग से रंगा जाता है, तो ऊपर से देखने पर कितने भिन्न प्रतिरूप (पैटर्न) संभव हैं?

Correct Option: (a) 2

The rectangular table top has dimensions 6' x 10'. Two rectangular portions of dimensions 2.5' x 8' are painted blue, and each has exactly two sides common with two edges of the table top. Since the table top has dimensions 6 by 10, let's place the 2.5 x 8 blue rectangles. Each rectangle has length 8 and width 2.5. Since the table length is 10, an 8-unit side can lie along the 10-unit edge of the table. The width is 2.5, and the table width is 6. Two such rectangles are painted. Since each has two sides common with table edges, they can be placed along the top edge and bottom edge (touching the 10-unit edges) or left and right edges. Specifically, because the dimensions are 2.5 x 8, and table is 6 x 10: An 8-unit side must align with the 10-unit edge (leaving 2 units of length uncovered on each side, or aligned to one end). But wait, since the table is fixed to the ground and viewed from above, how many different patterns are possible? The two blue portions can be placed symmetrically or mirrored. Specifically, because there are two identical blue regions of 2.5 x 8 on a 6 x 10 table, they can either occupy the top and bottom bands (each of width 2.5, leaving a white strip of 1.0 in the middle) or left and right bands. Since the table is fixed to the ground and viewed from above, orientation matters. There are 2 possible distinct visual patterns (e.g., horizontal bands vs vertical bands, or specific symmetrical placements). Thus, the number of possible patterns is 2.