Paper Folding, Punched Holes & Figure Counting Quiz: Reasoning

Spoilers! These are the Starter quiz’s answers. Easy, Medium, Hard and Mixed rounds show their own answers when you finish.

1. A square sheet is folded once along its vertical middle line, and one hole is punched through both layers away from the fold. How many holes appear when it is unfolded?

   • 1
   • 3
   • 2
   • 4

   Answer: 2. One punch passes through two layers, so two holes appear, mirror images of each other about the fold line.

2. A square sheet is folded in half and then in half again, making four layers. One hole is punched through all layers. How many holes appear when it is unfolded?

   • 4
   • 2
   • 8
   • 3

   Answer: 4. Each fold doubles the layers: 1 → 2 → 4. One punch through 4 layers gives 4 holes.

3. A square sheet is folded along a diagonal into a triangle, then folded again into a smaller triangle. Two holes are punched through all layers. How many holes appear when it is unfolded?

   • 4
   • 6
   • 2
   • 8

   Answer: 8. Two folds make 4 layers, and each of the 2 punches goes through all 4 layers: 2 × 4 = 8 holes.

4. A sheet is folded in half and a semicircle is cut out with its straight edge on the fold line. What does the unfolded sheet show?

   • Two semicircular holes
   • One full circular hole
   • Two full circular holes
   • A semicircular notch at the edge

   Answer: One full circular hole. The two halves of the cut join at the fold, so the semicircle opens into one complete circle.

5. A sheet is folded in half and one hole is punched exactly on the fold line. How many holes appear when it is unfolded?

   • 2
   • 0
   • 4
   • 1

   Answer: 1. A hole centred on the crease cuts both layers at the same place on the fold, so it opens out as a single hole on the crease line.

6. A triangle has two straight lines drawn from its top vertex to the base, dividing the base into three parts. How many triangles are there in the figure?

   • 5
   • 4
   • 6
   • 7

   Answer: 6. With the base in 3 parts, the triangles are 3 + 2 + 1 = 6 (each uses a group of adjacent parts).

7. A rectangle is divided into 4 equal smaller rectangles by one horizontal and one vertical line. How many rectangles are there in total?

   • 9
   • 5
   • 8
   • 4

   Answer: 9. Choose 2 of the 3 vertical lines and 2 of the 3 horizontal lines: 3 × 3 = 9 rectangles.

8. A square has both its diagonals drawn. How many triangles are there in the figure?

   • 4
   • 8
   • 6
   • 10

   Answer: 8. There are 4 small triangles meeting at the centre, plus 4 larger triangles each made of two small ones (each half of the square): 8.

9. How many squares of all sizes are there in a 3 × 3 grid of equal small squares?

   • 9
   • 13
   • 14
   • 12

   Answer: 14. Small: 9; 2 × 2 squares: 4; the whole 3 × 3: 1. Total 9 + 4 + 1 = 14.

10. A figure must be symmetric about a vertical line. Its left half has a small circle at the top-left corner and a triangle at the bottom-left corner. What must the right half contain?

    • A triangle at top-right and a circle at bottom-right
    • A triangle at top-right and a triangle at bottom-right
    • A circle at top-right only
    • A circle at top-right and a triangle at bottom-right

    Answer: A circle at top-right and a triangle at bottom-right. Reflection across a vertical line keeps each shape at the same height and moves it to the opposite side.