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/three positions
very commonTwo or three drawings of the same die; ask the face opposite X.
How to solve: Strike out the faces seen with X, or use the two-common-faces / same-position rules.
Example: Q. Two views share A and B; the other faces are C and D. Opposite of C?
D.
Standard die (sum 7)
occasionalThe die is stated to be standard or ordinary.
How to solve: Opposite pairs 1–6, 2–5, 3–4; hidden faces sum to 21 minus the shown three.
Example: Q. A standard die shows 2, 3 and 6. Sum of the hidden faces?
21 − 11 = 10.
Possible view of a labelled die
occasionalOpposite pairs are given in words; options are views.
How to solve: A view can never show two opposite faces; pick the option with one face from each pair.
Example: Q. A–D, B–E, C–F are pairs. Which view is possible?
The one showing A, B, C.
Opposite faces in a net
very commonAn unfolded sheet of six labelled squares.
How to solve: Skip one in a line; ends of a Z; leftovers form the last pair.
Example: Q. Row A, B, C, D. Opposite of B?
D.
Which cube can be formed
commonNet in the question, four cubes in the options.
How to solve: Reject cubes showing an opposite pair; then match the corner order by folding.
Example: Q. Which of the four cubes can be made from the net?
The only one without an opposite pair and with the correct corner order.
Which cube cannot be formed
occasionalSame figures, reversed question.
How to solve: Three options are formable; the impossible one shows an opposite pair or a mirrored corner.
Example: Q. Which cube cannot be made?
The one whose three faces run in the reverse order around the corner.
Painted cube cut into n³ pieces
very commonA painted cube of side n is cut into unit cubes.
How to solve: Use 8 / 12(n − 2) / 6(n − 2)² / (n − 2)³ and the n³ total check.
Example: Q. Side 4, painted, cut. How many cubes have two painted faces?
12 × 2 = 24.
Painted cuboid
commonThe block is a × b × c.
How to solve: Edges 4[(a−2)+(b−2)+(c−2)]; core (a−2)(b−2)(c−2); corners 8.
Example: Q. 5 × 4 × 3, painted, cut. Cubes with no painted face?
(3)(2)(1) = 6.