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ABHYAS PREP: NON-VERBAL REASONING · PAPER FOLDING

Paper folding and punching

Unfolding a crease adds the mirror image of every hole in that crease. Undo the folds from last to first; each fold doubles the number of holes.

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Worked examples

Example 1 · level 1

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

Answer: A

Example 2 · level 2

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
Show solution
  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 3, column 2.
  4. Undo the folds from last to first, reflecting every hole in the crease each time. That gives 4 holes: row 3, column 2; row 3, column 3; row 2, column 2; row 2, column 3.
  5. Only figure (C) has exactly these holes.

Answer: C

Example 3 · level 3

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

Answer: C

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