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Cube & Dice - Intermediate Level: multi-step reasoning INTERMEDIATE

Master cube & dice concepts through this excellence pursuit practice set. Worksheet 16 of 30 contains 20 intermediate-level problems. Deep dive into multi-step reasoning while learning logical thinking, problem solving, practice tests. Recommended for mid-level learners aiming for moderate complexity with mixed patterns.

📝 Worksheet 16 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Cube & Dice
Worksheet 16 of 30 (53% complete)

Question 1

This net folds into a standard dice. Dice Net5?3641 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 2.
net, completion, missing-face

Question 2

In a standard dice, opposite faces sum to 7. 5 dice in a rectangular arrangement. What is the sum of numbers on all visible faces?
Total sum on 5 dice = 5 × 21 = 105
Hidden faces = 14
Each hidden face has its opposite hidden (sum = 7)
Hidden sum = 14 × 3.5 = 49.0
Visible sum = 105 - 49.0 = 56
multiple-dice, summation, visible-faces, advanced

Question 3

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 4

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

Question 5

This net folds into a alternate dice. Dice Net125463 If face 4 is on the top, which face is on the bottom?
In a alternate dice, opposite faces are: 1↔4, 2↔3, 5↔6.
Face 4 is opposite to face 1.
When the net is folded, the face opposite to 4 will be on the bottom.
net, folding, spatial

Question 6

This net folds into a custom dice. Dice Net5?1632 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 4.
net, completion, missing-face

Question 7

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

Question 8

In a standard 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 9

A custom dice starts with: • Top: 1, Front: 2 It is rotated: rotate forward → rotate left → rotate counterclockwise → rotate clockwise Current Orientation5Top6Front3Right What number is on the TOP face after these rotations?
Initial: Top=1, Front=2
Rotation sequence: F → L → CC → C
After applying all rotations, Top=5, Front=6, Right=3
rotation, sequence, orientation

Question 10

Which dice configuration matches this net? Dice Net342561
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 11

A custom dice starts with: • Top: 1, Front: 2 It is rotated: rotate clockwise → rotate left → rotate right Current Orientation1Top4Front2Right What number is on the TOP face after these rotations?
Initial: Top=1, Front=2
Rotation sequence: C → L → R
After applying all rotations, Top=1, Front=4, Right=2
rotation, sequence, orientation

Question 12

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

Question 13

Which dice configuration matches this net? Dice Net362154
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 14

In a alternate dice, if face 1 is visible, which of the following CANNOT be adjacent to it?
In a alternate dice, opposite faces are never adjacent.
Face 1 is opposite to face 4.
Therefore, Face 4 cannot be adjacent to 1.
adjacent, faces, basic

Question 15

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

Question 16

This net folds into a standard dice. Dice Net253416 If face 1 is on the top, which face is on the bottom?
In a standard dice, opposite faces are: 1↔6, 2↔5, 3↔4.
Face 1 is opposite to face 6.
When the net is folded, the face opposite to 1 will be on the bottom.
net, folding, spatial

Question 17

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

Question 18

This net folds into a alternate dice. Dice Net152634 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 19

This net folds into a alternate dice. Dice Net25346? 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 1.
net, completion, missing-face

Question 20

A alternate dice starts with: • Top: 1, Front: 2 It is rotated: rotate clockwise → rotate forward → rotate right Current Orientation3Top3Front1Right What number is on the TOP face after these rotations?
Initial: Top=1, Front=2
Rotation sequence: C → F → R
After applying all rotations, Top=3, Front=3, Right=1
rotation, sequence, orientation
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