Consider a cube made by folding a single sheet of paper of appropriate shape. The interior faces of the cube are all blank. However, the exterior faces that are not visible in the above view may not be blank. Which one of the following represents a possible unfolding of the cube? A. [Net with marks on non-adjacent faces matching the visible cube faces] B. [Net with conflicting pattern placement] C. [Net with marks on opposite faces that contradict the cube view] D. [Net with mismatched face positions]
GATE 2022 · General Aptitude · Paper Folding · medium
Answer: Option A is the valid unfolding. Its patterned faces map correctly to the exterior faces of the cube visible in the given view.
- Identify the visible cube faces and their patterns: From the given cube view, three exterior faces are visible with distinct patterns. The three hidden exterior faces may or may not be patterned. All interior faces are blank.
- Test each net by tracing face positions: For each option, assign labels (Top, Bottom, Front, Back, Left, Right) to the net squares by following the fold sequence. Compare the patterned squares in the net to the required exterior face positions.
- Eliminate options with contradictions: Options B, C, D place patterned squares at positions that would land on the wrong face or create a contradiction with the blank-interior constraint when the net is folded. Option A places patterns only on exterior faces consistent with the given cube view.