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Cube & Dice - Expert Level: shortcut methods EXPERT

Comprehensive self assessment worksheet covering 20 expert-level cube & dice problems. Worksheet 28 of 30 emphasizes shortcut methods. Master aptitude training, reasoning skills, logical ability through detailed explanations. Difficulty: challenging problems and time-bound practice. Tailored for expert-level preparation.

📝 Worksheet 28 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Expert level

What you'll learn in this worksheet:
Your progress through Cube & Dice
Worksheet 28 of 30 (93% complete)

Question 1

Three faces of a custom dice meet at a vertex: 5, 1, and 4. Which face is opposite to face 5?
In a custom dice, opposite pairs are fixed.
Face 5 is opposite to face 2.
At the vertex where 5, 1, and 4 meet, the opposite face 2 is not visible.
vertex, opposite, 3d-reasoning, advanced

Question 2

In a custom dice, opposite faces sum to 7. 3 dice in a rectangular arrangement. What is the sum of numbers on all visible faces?
Total sum on 3 dice = 3 × 21 = 63
Hidden faces = 10
Each hidden face has its opposite hidden (sum = 7)
Hidden sum = 10 × 3.5 = 35.0
Visible sum = 63 - 35.0 = 28
multiple-dice, summation, visible-faces, advanced

Question 3

This net folds into a alternate dice. Dice Net354621 If face 5 is on the top, which face is on the bottom?
In a alternate dice, opposite faces are: 1↔4, 2↔3, 5↔6.
Face 5 is opposite to face 6.
When the net is folded, the face opposite to 5 will be on the bottom.
net, folding, spatial

Question 4

A standard dice starts with: • Top: 1, Front: 2 It is rotated: rotate right → rotate counterclockwise Current Orientation1Top2Front3Right What number is on the TOP face after these rotations?
Initial: Top=1, Front=2
Rotation sequence: R → CC
After applying all rotations, Top=1, Front=2, Right=3
rotation, sequence, orientation

Question 5

Which dice configuration matches this net? Dice Net356412
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 6

This net folds into a custom dice. Dice Net3142?6 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 5.
net, completion, missing-face

Question 7

This net folds into a standard dice. Dice Net45?362 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 1.
net, completion, missing-face

Question 8

Which dice configuration matches this net? Dice Net621543
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 9

Two views of a alternate dice are shown: View 1: Top=1, Front=2 View 2: Top=3, Front=5 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 10

This net folds into a alternate dice. Dice Net2453?6 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 11

Which dice configuration matches this net? Dice Net354612
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 12

A alternate dice starts with: • Top: 1, Front: 2 It is rotated: rotate counterclockwise → rotate right → rotate left → rotate forward Current Orientation4Top1Front3Right What number is on the TOP face after these rotations?
Initial: Top=1, Front=2
Rotation sequence: CC → R → L → F
After applying all rotations, Top=4, Front=1, Right=3
rotation, sequence, orientation

Question 13

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

Question 14

Two views of a alternate dice are shown: View 1: Top=6, Front=3 View 2: Top=4, 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 15

This net folds into a standard dice. Dice Net342516 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 16

This net folds into a alternate dice. Dice Net14526? 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 3.
net, completion, missing-face

Question 17

This net folds into a custom dice. Dice Net?62154 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 3.
net, completion, missing-face

Question 18

Three faces of a standard dice meet at a vertex: 2, 3, and 6. 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, 3, and 6 meet, the opposite face 5 is not visible.
vertex, opposite, 3d-reasoning, advanced

Question 19

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 20

Three faces of a alternate dice meet at a vertex: 3, 4, and 5. 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, 4, and 5 meet, the opposite face 2 is not visible.
vertex, opposite, 3d-reasoning, advanced
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