Cube & Dice
🔒 Log in to trackDice questions ask for opposite faces from several positions (adjacent-four, two-common-faces and same-position rules), or from an unfolded net (skip one; ends of a Z). Painted-cube questions use 8, 12(n−2), 6(n−2)² and (n−2)³.
One page per subtopic: detailed notes, every question type, formulas, tricks and practice sets.
Every formula on one printable page, grouped by subtopic.
4 exam-level questions worked step by step.
52 questions — untimed practice or a timed test with analysis.
Track record in the exam
Questions per shift in recent SSC CGL papers.
Test difficulty mix (52 questions)
Question patterns exams keep repeating
Taken from previous-year papers. If a pattern is marked "very common", expect to see it in your exam.
Opposite face from two views
very commonTwo or three pictures of the same die, and you must find the face opposite a given face.
Look for faces that appear in both views.
If two faces are common, the other two faces are opposite each other.
View 1 of a die shows A, B, C. View 2 shows A, C, D. Which face is opposite B?
A and C are in both views
B and D are the other faces next to A and C
So B and D are opposite
Answer: D
Standard die
occasionalThe die is called standard, so opposite faces add up to 7.
Opposite pairs: 1–6, 2–5, 3–4.
Find each hidden face as 7 minus the face opposite it.
A standard die shows 2, 3 and 6. What is the sum of the three hidden faces?
Opposite of 2 is 7 − 2 = 5
Opposite of 3 is 4, opposite of 6 is 1
5 + 4 + 1
Answer: 10
Which view is possible
occasionalOpposite pairs are given in words, and the options are sets of faces seen together.
Three faces seen together can never include an opposite pair.
Reject any option that shows both faces of a pair.
Opposite pairs are A–D, B–E, C–F. Which set of faces can be seen together: (a) A, D, B (b) A, B, C?
(a) has A and D, which are opposite, so it is impossible
(b) has A, B, C from three different pairs
So (b) is possible
Answer: (b) A, B, C
Opposite faces in a net
very commonAn unfolded flat sheet of six labelled squares.
In a row of squares, two squares with one square between them are opposite.
The last two left over are also opposite.
A net has a row of four squares A, B, C, D. E is above B and F is below B. Which face is opposite A?
In the row, squares with one between them are opposite
A and C have B between them
So A and C are opposite
Answer: C
Which cube can be made
commonA net is given, and the options are cubes made from it.
Find the opposite pairs in the net.
Reject any cube that shows two opposite faces together.
In a net, 1–6, 2–5 and 3–4 are opposite pairs. Which cube can be made: (a) showing 1, 6, 3 (b) showing 1, 2, 3?
(a) shows 1 and 6, which are opposite, so it is impossible
(b) shows 1, 2, 3 from three different pairs
So (b) can be made
Answer: (b)
Which cube cannot be made
occasionalSame kind of question, but you must find the cube that cannot be made.
Three options can be made.
The one that shows an opposite pair together is the answer.
In a net, P–S, Q–T and R–U are opposite pairs. Which cube cannot be made: (a) showing P, Q, R (b) showing P, S, Q?
(a) P, Q, R are from three different pairs, so it is possible
(b) P and S are opposite and cannot be seen together
Answer: (b)
Painted cube cut into small cubes
very commonA big cube is painted, then cut into small cubes of equal size.
For side n: 3 faces painted = 8, 2 faces = 12(n − 2), 1 face = 6(n − 2)², no face = (n − 2)³.
The four counts add up to n³.
A cube of side 4 is painted and cut into 1 × 1 × 1 cubes. How many cubes have exactly two painted faces?
Two painted faces means cubes on the edges, not the corners
Each edge has 4 − 2 = 2 such cubes
12 edges × 2
Answer: 24
Painted block (cuboid)
commonA painted block of size a × b × c is cut into small cubes.
Cubes with no paint are the inside block: (a − 2)(b − 2)(c − 2).
There are always 8 corner cubes with 3 painted faces.
A 5 × 4 × 3 block is painted and cut into 1 × 1 × 1 cubes. How many cubes have no painted face?
Remove one layer from each side: 5 − 2 = 3, 4 − 2 = 2, 3 − 2 = 1
Inside block is 3 × 2 × 1
Answer: 6