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Cube & Dice - Intermediate Level: critical thinking INTERMEDIATE

Comprehensive weakness targeting worksheet covering 20 intermediate-level cube & dice problems. Worksheet 18 of 30 emphasizes critical thinking. Master practice tests, exam preparation, competitive exams through detailed explanations. Difficulty: moderate complexity with mixed patterns. Tailored for mid-level preparation.

📝 Worksheet 18 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Cube & Dice
Worksheet 18 of 30 (60% complete)

Question 1

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 2

This net folds into a alternate dice. Dice Net16?354 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 3

A standard dice starts with: • Top: 1, Front: 2 It is rotated: rotate counterclockwise → rotate left → rotate clockwise → rotate backward Current Orientation3Top6Front5Right What number is on the TOP face after these rotations?
Initial: Top=1, Front=2
Rotation sequence: CC → L → C → B
After applying all rotations, Top=3, Front=6, Right=5
rotation, sequence, orientation

Question 4

This net folds into a custom dice. Dice Net426135 If face 3 is on the top, which face is on the bottom?
In a custom dice, opposite faces are: 1↔3, 2↔5, 4↔6.
Face 3 is opposite to face 1.
When the net is folded, the face opposite to 3 will be on the bottom.
net, folding, spatial

Question 5

In a custom dice, if face 2 is visible, which of the following CANNOT be adjacent to it?
In a custom dice, opposite faces are never adjacent.
Face 2 is opposite to face 5.
Therefore, Face 5 cannot be adjacent to 2.
adjacent, faces, basic

Question 6

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 7

This net folds into a standard dice. Dice Net412536 If face 4 is on the top, which face is on the bottom?
In a standard dice, opposite faces are: 1↔6, 2↔5, 3↔4.
Face 4 is opposite to face 3.
When the net is folded, the face opposite to 4 will be on the bottom.
net, folding, spatial

Question 8

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 9

This net folds into a standard dice. Dice Net?41625 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 10

In a custom dice, opposite faces sum to 7. 4 dice arranged in a 2×2 grid. 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 11

Three faces of a standard dice meet at a vertex: 1, 4, and 5. Which face is opposite to face 1?
In a standard dice, opposite pairs are fixed.
Face 1 is opposite to face 6.
At the vertex where 1, 4, and 5 meet, the opposite face 6 is not visible.
vertex, opposite, 3d-reasoning, advanced

Question 12

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

Question 13

Three faces of a custom dice meet at a vertex: 3, 4, and 2. Which face is opposite to face 3?
In a custom dice, opposite pairs are fixed.
Face 3 is opposite to face 1.
At the vertex where 3, 4, and 2 meet, the opposite face 1 is not visible.
vertex, opposite, 3d-reasoning, advanced

Question 14

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

Question 15

A custom dice starts with: • Top: 1, Front: 2 It is rotated: rotate right → rotate left → rotate backward Current Orientation2Top3Front6Right What number is on the TOP face after these rotations?
Initial: Top=1, Front=2
Rotation sequence: R → L → B
After applying all rotations, Top=2, Front=3, Right=6
rotation, sequence, orientation

Question 16

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

Question 17

Two views of a alternate dice are shown: View 1: Top=1, Front=5 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

Question 18

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

Question 19

In a alternate dice, if face 3 is visible, which of the following CANNOT be adjacent to it?
In a alternate dice, opposite faces are never adjacent.
Face 3 is opposite to face 2.
Therefore, Face 2 cannot be adjacent to 3.
adjacent, faces, basic

Question 20

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