The paper pattern below is folded along its lines into a cube. Find the number of dots on the face opposite the face with five dots.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Four
When a sheet like this is folded into a cube, two squares in a straight line with one square between them become opposite faces, and the two squares on either side of the row of four fold onto the two side faces, which are also opposite. In the picture each pair has its own colour.
The 3-dot face and the 2-dot face: one square between them in the row
The 5-dot face and the 4-dot face: one square between them in the row
The 6-dot face and the 1-dot face: one square between them, on the two sides of the row
So the face opposite the 5-dot face is the 4-dot face.
Why the other options are incorrect
Option (1) One — Incorrect. The 1-dot face is opposite the 6-dot face (one square between them, on the two sides of the row).
Option (2) Six — Incorrect. The 6-dot face is opposite the 1-dot face (one square between them, on the two sides of the row).
Option (4) Two — Incorrect. The 2-dot face shares an edge with the 5-dot face on the sheet, so the two meet on the cube.