Paper Folding and Punchingकागज़ मोड़ना और छेद करना questions and answersप्रश्न और उत्तर

How paper folding and punching worksकागज़ मोड़ना और छेद करना को समझिए

When the sheet is folded, the punch goes through every layer. Opening one crease reveals the layer that was folded underneath, and the holes in that layer are mirror images of the top holes in the crease. So a hole near the crease has a partner near the crease; a hole near the edge has a partner near the opposite edge.

With two folds, undo them in reverse order: first the last fold, then the first. Each unfolding doubles the number of holes, so one punch through a sheet folded twice gives four holes, symmetric about both creases.

A diagonal crease is a mirror too, just a slanted one. Folding along the diagonal from the top-left corner to the bottom-right corner swaps the across and down positions of every hole: a hole in row 1, column 3 has a partner in row 3, column 1.

Each trick says when to use it, why it works and when it fails. Formula tricks are checked by code over their whole range.हर ट्रिक बताती है कि उसे कब इस्तेमाल करें, वह क्यों काम करती है और कब नहीं। सूत्र वाली ट्रिक्स को कोड से उनकी पूरी रेंज पर जाँचा गया है।

Answers and full solutions are shown. Hide them to test yourself first.उत्तर और पूरे हल दिखाए गए हैं। पहले खुद को परखने के लिए इन्हें छिपाइए।

1. Example 1उदाहरण 1 · Paper folding and punching · Easyआसान

   A square sheet of paper is folded along the dashed line, and holes are punched through every layer. Which figure shows the sheet when it is opened out?

   1. A
   2. B
   3. C
   4. D
   Answer:उत्तर: D

   1. Fold 1: along the horizontal centre line, top half down onto the bottom half.
   2. Punched: row 3, column 1.
   3. Undo the folds from last to first, reflecting every hole in the crease each time. That gives 2 holes: row 3, column 1; row 2, column 1.
   4. Only figure (D) has exactly these holes.

2. Example 2उदाहरण 2 · Paper folding and punching · Mediumमध्यम

   A square sheet of paper is folded twice, in the order shown, and holes are punched through every layer. Which figure shows the sheet when it is opened out?

   1. A
   2. B
   3. C
   4. D
   Answer:उत्तर: C

   1. Fold 1: along the horizontal centre line, top half down onto the bottom half.
   2. Fold 2: along the vertical centre line, right half over onto the left half.
   3. Punched: row 4, column 2.
   4. Undo the folds from last to first, reflecting every hole in the crease each time. That gives 4 holes: row 4, column 2; row 4, column 3; row 1, column 2; row 1, column 3.
   5. Only figure (C) has exactly these holes.

3. Example 3उदाहरण 3 · Paper folding and punching · Hardकठिन

   A square sheet of paper is folded along the dashed line, and holes are punched through every layer. Which figure shows the sheet when it is opened out?

   1. A
   2. B
   3. C
   4. D
   Answer:उत्तर: D

   1. Fold 1: along the diagonal from top-left to bottom-right, the top-right half onto the bottom-left half.
   2. Punched: row 3, column 1 and row 5, column 4.
   3. Undo the folds from last to first, reflecting every hole in the crease each time. That gives 4 holes: row 3, column 1; row 5, column 4; row 1, column 3; row 4, column 5.
   4. Only figure (D) has exactly these holes.

4. Example 4उदाहरण 4 · Paper folding and punching · Mediumमध्यम

   A square sheet of paper is folded twice, in the order shown, and holes are punched through every layer. Which figure shows the sheet when it is opened out?

   1. A
   2. B
   3. C
   4. D
   Answer:उत्तर: D

   1. Fold 1: along the horizontal centre line, bottom half up onto the top half.
   2. Fold 2: along the vertical centre line, left half over onto the right half.
   3. Punched: row 1, column 3 and row 2, column 3.
   4. Undo the folds from last to first, reflecting every hole in the crease each time. That gives 8 holes: row 1, column 3; row 2, column 3; row 1, column 2; row 2, column 2; row 4, column 3; row 3, column 3; row 4, column 2; row 3, column 2.
   5. Only figure (D) has exactly these holes.

5. Example 5उदाहरण 5 · Paper folding and punching · Mediumमध्यम

   A square sheet of paper is folded twice, in the order shown, and holes are punched through every layer. Which figure shows the sheet when it is opened out?

   1. A
   2. B
   3. C
   4. D
   Answer:उत्तर: D

   1. Fold 1: along the vertical centre line, left half over onto the right half.
   2. Fold 2: along the horizontal centre line, top half down onto the bottom half.
   3. Punched: row 4, column 3.
   4. Undo the folds from last to first, reflecting every hole in the crease each time. That gives 4 holes: row 4, column 3; row 1, column 3; row 4, column 2; row 1, column 2.
   5. Only figure (D) has exactly these holes.

6. Example 6उदाहरण 6 · Paper folding and punching · Mediumमध्यम

   A square sheet of paper is folded twice, in the order shown, and holes are punched through every layer. Which figure shows the sheet when it is opened out?

   1. A
   2. B
   3. C
   4. D
   Answer:उत्तर: B

   1. Fold 1: along the horizontal centre line, bottom half up onto the top half.
   2. Fold 2: along the vertical centre line, left half over onto the right half.
   3. Punched: row 2, column 4 and row 1, column 3.
   4. Undo the folds from last to first, reflecting every hole in the crease each time. That gives 8 holes: row 2, column 4; row 1, column 3; row 2, column 1; row 1, column 2; row 3, column 4; row 4, column 3; row 3, column 1; row 4, column 2.
   5. Only figure (B) has exactly these holes.

Common mistakesआम गलतियाँ

• Copying holes by sliding them across the crease instead of reflecting them, which reverses their order.
• Undoing only one fold of two, so the answer has half the holes it should.
• Reflecting across the wrong line, for example the vertical centre line when the paper was folded top to bottom.

Frequently asked questionsअक्सर पूछे जाने वाले प्रश्न