Paper Folding and Cutting
About 6 min · Reasoning Ability · English
Time worked out from the lesson's 388 words at 150 words a minute, plus a minute for each question.
Paper folding and cutting is a visual reasoning topic that tests your ability to mentally manipulate shapes and predict outcomes. In HSSC CET, these questions are considered scoring once you understand the underlying logic.
Key ideas
- Fold line acts as a mirror: When paper is unfolded, any cut or punch reflects symmetrically across the fold line. This is the fundamental principle.
- Number of holes doubles with each fold: One punch on a twice-folded paper creates 4 holes (2¹ × 2¹ = 4). On a thrice-folded paper, one punch creates 8 holes.
- Distance from fold line is preserved: A hole punched 1 cm from the fold appears 1 cm on the other side too when unfolded.
- Track the folding sequence: Unfold in exact reverse order of folding. The last fold opens first.
- Corner folds create diagonal symmetry: When paper is folded diagonally, holes reflect along the diagonal axis.
Watch out for
- Ignoring fold direction → Always note whether fold is left-to-right, bottom-to-top, or diagonal. Each creates different symmetry axes. Draw arrows to track direction.
- Unfolding in wrong order → Students unfold in the same sequence as folding. Correct approach: reverse the order—last fold opens first.
- Miscounting holes → Assuming one punch = one hole regardless of layers. Count layers at the punch point; each layer produces one hole.
Quick reference
- One fold = 2 holes; two folds = 4 holes; three folds = 8 holes (from single punch)
- Unfold in reverse order of folding
- Holes reflect symmetrically across each fold line
- Distance from fold line stays equal on both sides
- Diagonal fold = diagonal line of symmetry
Check yourself: 3 questions
1. A square sheet of paper is folded once in half and then a circular hole is punched through all the layers. When the paper is unfolded, how many holes will appear on the sheet?
2. A rectangular sheet of paper is folded twice (first in half, then in half again) to form a smaller rectangle. A triangular piece is cut from one corner through all layers. When the paper is completely unfolded, how many triangular cuts will be visible?
3. A square sheet of paper is folded twice: first along the diagonal and then along the median of the resulting triangle. A circular hole is punched through all layers. When unfolded, how many holes will appear on the paper?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
Read the full noteFlashcards for this topic
Saves this lesson and its 3 questions in this browser on this phone. No sign-in; nothing about you is saved or sent. A saved copy is not updated until you save it again. Parts that load from the server when you use them (the AI tutor, adaptive practice, sign-in) still need a connection.