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Cube & Dice - Advanced Level: quick solving techniques ADVANCED

Exam-focused holistic practice ★ worksheet: 20 advanced-level cube & dice questions. Worksheet 23 of 30 targets quick solving techniques. Build proficiency in logical thinking, problem solving, practice tests with detailed solutions. Ideal for advanced competitive exam preparation.

📝 Worksheet 23 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Advanced level

What you'll learn in this worksheet:
Your progress through Cube & Dice
Worksheet 23 of 30 (76% complete)

Question 1

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

Question 2

This net folds into a alternate dice. Dice Net5142?3 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 6.
net, completion, missing-face

Question 3

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

Question 4

This net folds into a alternate dice. Dice Net16253? 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 4.
net, completion, missing-face

Question 5

This net folds into a standard dice. Dice Net4321?6 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 5.
net, completion, missing-face

Question 6

Which dice configuration matches this net? Dice Net453612
This net forms a custom dice. When folded, opposite faces are: 1↔3, 2↔5, 4↔6. In the net, opposite faces are never adjacent.
net, unfolding, spatial, basic

Question 7

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

Question 8

This net folds into a standard dice. Dice Net146253 If face 2 is on the top, which face is on the bottom?
In a standard dice, opposite faces are: 1↔6, 2↔5, 3↔4.
Face 2 is opposite to face 5.
When the net is folded, the face opposite to 2 will be on the bottom.
net, folding, spatial

Question 9

This net folds into a custom dice. Dice Net465132 If face 1 is on the top, which face is on the bottom?
In a custom dice, opposite faces are: 1↔3, 2↔5, 4↔6.
Face 1 is opposite to face 3.
When the net is folded, the face opposite to 1 will be on the bottom.
net, folding, spatial

Question 10

A standard dice starts with: • Top: 1, Front: 2 It is rotated: rotate counterclockwise → rotate backward → rotate clockwise Current Orientation3Top2Front6Right What number is on the TOP face after these rotations?
Initial: Top=1, Front=2
Rotation sequence: CC → B → C
After applying all rotations, Top=3, Front=2, Right=6
rotation, sequence, orientation

Question 11

In a custom dice, if face 6 is visible, which of the following CANNOT be adjacent to it?
In a custom dice, opposite faces are never adjacent.
Face 6 is opposite to face 4.
Therefore, Face 4 cannot be adjacent to 6.
adjacent, faces, basic

Question 12

In a custom dice, opposite faces sum to 7. 2 dice stacked vertically. What is the sum of numbers on all visible faces?
Total sum on 2 dice = 2 × 21 = 42
Hidden faces = 4
Each hidden face has its opposite hidden (sum = 7)
Hidden sum = 4 × 3.5 = 14.0
Visible sum = 42 - 14.0 = 28
multiple-dice, summation, visible-faces, advanced

Question 13

A custom dice starts with: • Top: 1, Front: 2 It is rotated: rotate forward → rotate backward Current Orientation1Top2Front6Right What number is on the TOP face after these rotations?
Initial: Top=1, Front=2
Rotation sequence: F → B
After applying all rotations, Top=1, Front=2, Right=6
rotation, sequence, orientation

Question 14

In a custom dice, opposite faces sum to 7. 2 dice in a rectangular arrangement. What is the sum of numbers on all visible faces?
Total sum on 2 dice = 2 × 21 = 42
Hidden faces = 8
Each hidden face has its opposite hidden (sum = 7)
Hidden sum = 8 × 3.5 = 28.0
Visible sum = 42 - 28.0 = 14
multiple-dice, summation, visible-faces, advanced

Question 15

This net folds into a standard dice. Dice Net52361? 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 4.
net, completion, missing-face

Question 16

This net folds into a custom dice. Dice Net1436?5 What number should replace the '?' mark?
In a custom dice, the opposite pairs are: 1↔3, 2↔5, 4↔6.
Using the adjacency relationships and the visible numbers, the missing face must be 2.
net, completion, missing-face

Question 17

A custom dice starts with: • Top: 1, Front: 2 It is rotated: rotate forward → rotate backward → rotate clockwise → rotate counterclockwise Current Orientation1Top2Front6Right What number is on the TOP face after these rotations?
Initial: Top=1, Front=2
Rotation sequence: F → B → C → CC
After applying all rotations, Top=1, Front=2, Right=6
rotation, sequence, orientation

Question 18

This net folds into a alternate dice. Dice Net?51643 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 19

Which dice configuration matches this net? Dice Net235164
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 20

In a standard dice, opposite faces sum to 7. 2 dice arranged in a horizontal line. What is the sum of numbers on all visible faces?
Total sum on 2 dice = 2 × 21 = 42
Hidden faces = 4
Each hidden face has its opposite hidden (sum = 7)
Hidden sum = 4 × 3.5 = 14.0
Visible sum = 42 - 14.0 = 28
multiple-dice, summation, visible-faces, advanced
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