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Cube & Dice - Advanced Level: common mistakes to avoid ADVANCED

Master cube & dice concepts through this hard problem set practice set. Worksheet 26 of 30 contains 20 advanced-level problems. Deep dive into common mistakes to avoid while learning exam preparation, competitive exams, aptitude training. Recommended for advanced learners aiming for complex scenarios and multi-step problems.

📝 Worksheet 26 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Advanced level

What you'll learn in this worksheet:
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Worksheet 26 of 30 (86% complete)

Question 1

In a standard dice, opposite faces sum to 7. 4 dice stacked vertically. What is the sum of numbers on all visible faces?
Total sum on 4 dice = 4 × 21 = 84
Hidden faces = 8
Each hidden face has its opposite hidden (sum = 7)
Hidden sum = 8 × 3.5 = 28.0
Visible sum = 84 - 28.0 = 56
multiple-dice, summation, visible-faces, advanced

Question 2

A alternate dice starts with: • Top: 1, Front: 2 It is rotated: rotate counterclockwise → rotate forward → rotate backward → rotate left Current Orientation1Top3Front4Right What number is on the TOP face after these rotations?
Initial: Top=1, Front=2
Rotation sequence: CC → F → B → L
After applying all rotations, Top=1, Front=3, Right=4
rotation, sequence, orientation

Question 3

Three faces of a alternate dice meet at a vertex: 1, 6, and 3. Which face is opposite to face 1?
In a alternate dice, opposite pairs are fixed.
Face 1 is opposite to face 4.
At the vertex where 1, 6, and 3 meet, the opposite face 4 is not visible.
vertex, opposite, 3d-reasoning, advanced

Question 4

Three faces of a alternate dice meet at a vertex: 5, 1, and 3. Which face is opposite to face 5?
In a alternate dice, opposite pairs are fixed.
Face 5 is opposite to face 6.
At the vertex where 5, 1, and 3 meet, the opposite face 6 is not visible.
vertex, opposite, 3d-reasoning, advanced

Question 5

Two views of a standard dice are shown: View 1: Top=1, Front=4 View 2: Top=3, Front=5 Which face is opposite to face 1?
In a standard dice, opposite pairs are: 1↔6, 2↔5, 3↔4.
Face 1 is opposite to face 6.
opposite, multiple-views, deduction

Question 6

Which dice configuration matches this net? Dice Net651243
This net forms a standard dice. When folded, opposite faces are: 1↔6, 2↔5, 3↔4. In the net, opposite faces are never adjacent.
net, unfolding, spatial, basic

Question 7

Two views of a standard dice are shown: View 1: Top=4, Front=6 View 2: Top=6, Front=2 Which face is opposite to face 4?
In a standard dice, opposite pairs are: 1↔6, 2↔5, 3↔4.
Face 4 is opposite to face 3.
opposite, multiple-views, deduction

Question 8

This net folds into a custom dice. Dice Net241356 If face 6 is on the top, which face is on the bottom?
In a custom dice, opposite faces are: 1↔3, 2↔5, 4↔6.
Face 6 is opposite to face 4.
When the net is folded, the face opposite to 6 will be on the bottom.
net, folding, spatial

Question 9

In a alternate dice, if face 6 is visible, which of the following CANNOT be adjacent to it?
In a alternate dice, opposite faces are never adjacent.
Face 6 is opposite to face 5.
Therefore, Face 5 cannot be adjacent to 6.
adjacent, faces, basic

Question 10

This net folds into a alternate dice. Dice Net135?46 What number should replace the '?' mark?
In a alternate dice, the opposite pairs are: 1↔4, 2↔3, 5↔6.
Using the adjacency relationships and the visible numbers, the missing face must be 2.
net, completion, missing-face

Question 11

In a custom dice, opposite faces sum to 7. 4 dice arranged in a horizontal line. What is the sum of numbers on all visible faces?
Total sum on 4 dice = 4 × 21 = 84
Hidden faces = 10
Each hidden face has its opposite hidden (sum = 7)
Hidden sum = 10 × 3.5 = 35.0
Visible sum = 84 - 35.0 = 49
multiple-dice, summation, visible-faces, advanced

Question 12

Three faces of a alternate dice meet at a vertex: 1, 3, and 6. Which face is opposite to face 1?
In a alternate dice, opposite pairs are fixed.
Face 1 is opposite to face 4.
At the vertex where 1, 3, and 6 meet, the opposite face 4 is not visible.
vertex, opposite, 3d-reasoning, advanced

Question 13

This net folds into a standard dice. Dice Net5?1624 What number should replace the '?' mark?
In a standard dice, the opposite pairs are: 1↔6, 2↔5, 3↔4.
Using the adjacency relationships and the visible numbers, the missing face must be 3.
net, completion, missing-face

Question 14

This net folds into a alternate dice. Dice Net514623 If face 6 is on the top, which face is on the bottom?
In a alternate dice, opposite faces are: 1↔4, 2↔3, 5↔6.
Face 6 is opposite to face 5.
When the net is folded, the face opposite to 6 will be on the bottom.
net, folding, spatial

Question 15

Which dice configuration matches this net? Dice Net123564
This net forms a alternate dice. When folded, opposite faces are: 1↔4, 2↔3, 5↔6. In the net, opposite faces are never adjacent.
net, unfolding, spatial, basic

Question 16

Three faces of a standard dice meet at a vertex: 2, 6, and 4. Which face is opposite to face 2?
In a standard dice, opposite pairs are fixed.
Face 2 is opposite to face 5.
At the vertex where 2, 6, and 4 meet, the opposite face 5 is not visible.
vertex, opposite, 3d-reasoning, advanced

Question 17

Which dice configuration matches this net? Dice Net152346
This net forms a standard dice. When folded, opposite faces are: 1↔6, 2↔5, 3↔4. In the net, opposite faces are never adjacent.
net, unfolding, spatial, basic

Question 18

Three faces of a alternate dice meet at a vertex: 6, 2, and 4. Which face is opposite to face 6?
In a alternate dice, opposite pairs are fixed.
Face 6 is opposite to face 5.
At the vertex where 6, 2, and 4 meet, the opposite face 5 is not visible.
vertex, opposite, 3d-reasoning, advanced

Question 19

Two views of a custom dice are shown: View 1: Top=1, Front=5 View 2: Top=4, Front=2 Which face is opposite to face 1?
In a custom dice, opposite pairs are: 1↔3, 2↔5, 4↔6.
Face 1 is opposite to face 3.
opposite, multiple-views, deduction

Question 20

Two views of a alternate dice are shown: View 1: Top=1, Front=2 View 2: Top=3, Front=6 Which face is opposite to face 1?
In a alternate dice, opposite pairs are: 1↔4, 2↔3, 5↔6.
Face 1 is opposite to face 4.
opposite, multiple-views, deduction
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