Mirror Images, Folding & Cubes
18 Class 6 IMO Mathematics Olympiad practice questions on mirror images, folding & cubes, part of the Visual & Spatial Reasoning topic area. Every question below includes the correct answer and a full explanation.
Practice this topic interactively →1. Which of these letters looks the same in a mirror image (left-right flip)?
- A.F
- B.L
- C.M
- D.G
View this question on its own page →Show answer & explanation
Answer: C. M
M has a vertical line of symmetry, so it looks identical when mirror-flipped left-right. F, L, and G do not.
2. Which of these, when its mirror image (left-right flip) is taken, looks exactly the same as the original: the digit 0, 2, 3, or 7?
- A.0
- B.2
- C.3
- D.7
View this question on its own page →Show answer & explanation
Answer: A. 0
0 is symmetric left-to-right, so its mirror image looks identical. 2, 3, and 7 change shape when flipped.
3. A cube has faces numbered 1 to 6. Opposite faces always add to 7. Which number is opposite 4?
- A.1
- B.2
- C.3
- D.5
View this question on its own page →Show answer & explanation
Answer: C. 3
7 − 4 = 3, so 3 is opposite 4.
4. The time shown on a clock is 3:15. What time does its mirror image show?
- A.8:15
- B.8:45
- C.9:15
- D.9:45
View this question on its own page →Show answer & explanation
Answer: B. 8:45
A clock's mirror image shows a time such that original + mirrored = 12:00. 12:00 − 3:15 = 8:45.
5. A cube has its faces painted red, blue, green, yellow, white and black — one colour per face, opposite faces always differing. If red is opposite blue, and green is opposite yellow, which colour is opposite black?
- A.Red
- B.Green
- C.White
- D.Yellow
View this question on its own page →Show answer & explanation
Answer: C. White
The three pairs are Red-Blue, Green-Yellow, and the remaining two, Black and White, must be the last pair.
6. A square piece of paper is folded in half twice (into a small square), and one corner is snipped off. When unfolded, how many holes appear (assuming the snip passes through all layers, away from the fold edges)?
- A.1
- B.2
- C.4
- D.8
View this question on its own page →Show answer & explanation
Answer: C. 4
Folding twice creates 4 layers of paper. A single snip through all layers becomes 4 cut marks when unfolded.
7. How many small cubes in the same 3×3×3 cube have no painted faces at all?
- A.0
- B.1
- C.2
- D.4
View this question on its own page →Show answer & explanation
Answer: B. 1
Only the single cube at the very centre (1×1×1 core) touches none of the outer faces.
8. A rectangular sheet of paper is folded exactly in half along its longer side. If the original sheet was 20 cm by 12 cm, what are the dimensions of the folded sheet?
- A.10 cm × 12 cm
- B.20 cm × 6 cm
- C.10 cm × 6 cm
- D.20 cm × 12 cm
View this question on its own page →Show answer & explanation
Answer: A. 10 cm × 12 cm
Folding along the longer (20 cm) side halves that length to 10 cm, while the 12 cm side stays the same: 10 cm × 12 cm.
9. A dice (standard, opposite faces sum to 7) shows 5 on top and 3 facing you. Which number is on the bottom face?
- A.1
- B.2
- C.3
- D.4
View this question on its own page →Show answer & explanation
Answer: B. 2
Opposite faces of a standard die always add to 7. The bottom is opposite the top (5), so bottom = 7−5 = 2.
10. A die (opposite faces sum to 7) shows 4 on top. What number must be on the bottom face?
- A.1
- B.2
- C.3
- D.5
View this question on its own page →Show answer & explanation
Answer: C. 3
7 − 4 = 3.
11. A square sheet is folded once vertically and once horizontally. One hole is punched through the folded sheet, away from the folded edges. How many holes appear when it is fully unfolded?
- A.2
- B.3
- C.4
- D.8
View this question on its own page →Show answer & explanation
Answer: C. 4
Two folds create 4 layers, so one punch through all layers becomes 4 holes when unfolded, arranged symmetrically.
12. A cube is painted red on all its faces and then cut into 27 identical smaller cubes (3×3×3). How many of the small cubes have exactly 2 faces painted red?
- A.6
- B.8
- C.12
- D.24
View this question on its own page →Show answer & explanation
Answer: C. 12
In a 3×3×3 cube, the cubes with exactly 2 painted faces lie on the edges (excluding corners) — 1 per edge × 12 edges = 12.
13. In the same 3×3×3 painted cube cut into 27 pieces, how many small cubes have exactly 3 faces painted?
- A.4
- B.6
- C.8
- D.12
View this question on its own page →Show answer & explanation
Answer: C. 8
The corner cubes are the only ones touching 3 outer faces — a cube has 8 corners.
14. A wall clock shows 7:20 in a mirror placed in front of it. What is the actual time?
- A.4:20
- B.4:40
- C.5:20
- D.5:40
View this question on its own page →Show answer & explanation
Answer: B. 4:40
Since original + mirror image = 12:00, actual time = 12:00 − 7:20 = 4:40.
15. A strip of paper is folded in half 3 times, then unfolded completely. Into how many equal parts is the strip divided by the fold lines?
- A.4
- B.6
- C.8
- D.9
View this question on its own page →Show answer & explanation
Answer: C. 8
Each fold doubles the number of sections: 3 folds give 2³ = 8 equal parts.
16. A square sheet is folded in half twice. One hole is punched away from the folds. How many holes appear when unfolded?
- A.4
- B.2
- C.3
- D.8
View this question on its own page →Show answer & explanation
Answer: A. 4
Two folds create 4 layers, so one punch through all layers becomes 4 holes when unfolded.
17. A wooden cube is painted blue on the outside and then cut into 64 identical smaller cubes (4×4×4). How many small cubes have exactly 1 face painted?
- A.16
- B.24
- C.36
- D.48
View this question on its own page →Show answer & explanation
Answer: B. 24
On each face, the cubes with only 1 painted side form a (4−2)×(4−2)=2×2 patch — 4 per face × 6 faces = 24.
18. A cube is painted on all faces and cut into 27 equal cubes. How many small cubes have exactly two painted faces?
- A.24
- B.12
- C.6
- D.8
View this question on its own page →Show answer & explanation
Answer: B. 12
In a 3×3×3 cube, the cubes with exactly 2 painted faces lie on the edges (excluding corners) — 1 per edge × 12 edges = 12.