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Cube & Dice - Intermediate-Advanced Level: problem decomposition INTERMEDIATE-ADVANCED

Strategic expert challenge ★ for cube & dice: 20 intermediate-advanced-level problems. Worksheet 19 of 30 - Focus: problem decomposition. Develop expertise in exam preparation, competitive exams, aptitude training with step-by-step solutions. Ideal for advanced developing learners targeting advanced concepts with increasing complexity.

📝 Worksheet 19 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate-advanced level

What you'll learn in this worksheet:
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Worksheet 19 of 30 (63% complete)

Question 1

Two views of a custom dice are shown: View 1: Top=2, Front=6 View 2: Top=6, Front=1 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 Net1?4352 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

Which dice configuration matches this net? Dice Net264315
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 4

In a standard dice, if face 6 is visible, which of the following CANNOT be adjacent to it?
In a standard dice, opposite faces are never adjacent.
Face 6 is opposite to face 1.
Therefore, Face 1 cannot be adjacent to 6.
adjacent, faces, basic

Question 5

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

Question 6

In a standard dice, opposite faces sum to 7. 5 dice arranged in a horizontal line. What is the sum of numbers on all visible faces?
Total sum on 5 dice = 5 × 21 = 105
Hidden faces = 13
Each hidden face has its opposite hidden (sum = 7)
Hidden sum = 13 × 3.5 = 45.5
Visible sum = 105 - 45.5 = 59
multiple-dice, summation, visible-faces, advanced

Question 7

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

Question 8

Which dice configuration matches this net? Dice Net461325
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 9

Two views of a standard dice are shown: View 1: Top=3, Front=1 View 2: Top=4, Front=2 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 10

This net folds into a alternate dice. Dice Net523164 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 11

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

Question 12

This net folds into a custom dice. Dice Net251346 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 13

This net folds into a custom dice. Dice Net51?236 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 14

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

Question 15

In a custom dice, if face 1 is visible, which of the following CANNOT be adjacent to it?
In a custom dice, opposite faces are never adjacent.
Face 1 is opposite to face 3.
Therefore, Face 3 cannot be adjacent to 1.
adjacent, faces, basic

Question 16

Two views of a standard dice are shown: View 1: Top=1, Front=5 View 2: Top=3, Front=1 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 17

In a standard dice, if face 2 is visible, which of the following CANNOT be adjacent to it?
In a standard 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 18

Three faces of a standard dice meet at a vertex: 5, 4, and 1. 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, 4, and 1 meet, the opposite face 2 is not visible.
vertex, opposite, 3d-reasoning, advanced

Question 19

Three faces of a alternate dice meet at a vertex: 3, 1, and 6. 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, 1, and 6 meet, the opposite face 2 is not visible.
vertex, opposite, 3d-reasoning, advanced

Question 20

Which dice configuration matches this net? Dice Net532461
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
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