Cube and Dice Questions for AFCAT

Standard Dice Rules

A standard dice has 6 faces numbered 1 to 6. The most important rule: opposite faces always add up to 7. So 1 is opposite 6, 2 is opposite 5, and 3 is opposite 4. This is the single most tested fact. When a dice is shown in a diagram, you can find any hidden or opposite face using this rule instantly without drawing anything.

• Opposite pairs: 1-6, 2-5, 3-4 (all add to 7)
• A dice has 8 corners, 12 edges, 6 faces
• When two dice positions are shown, the face that is common (same number) helps you orient the other faces
• If the same number appears on two different positions, compare the adjacent faces to find what is opposite what
• Non-standard dice: ignore the 7-rule, use only the given diagrams to deduce opposite faces

Finding Opposite Faces from Diagrams

AFCAT often gives 2 or 3 positions of the same dice and asks which face is opposite a given face. The trick is to find one face that appears in both positions (the anchor). Keep that face fixed and rotate mentally to check which faces move. Alternatively, use the elimination method: if you can see both faces of a pair in the same view, they cannot be opposite each other.

• If a face is visible in one position, it cannot be opposite any face visible in that same position
• Use the anchor face (common in two views) to align orientation
• Faces adjacent in any one view are never opposite to each other
• With 3 views given, you can map all 3 opposite pairs even for non-standard dice
• Cross-check by elimination: 3 pairs total, find 2 and the third is automatic

Cube Painting and Cutting

A cube is painted on all 6 faces and then cut into smaller equal cubes. AFCAT asks how many small cubes have 3 faces painted, 2 faces painted, 1 face painted, or no face painted. The position of a small cube determines how many painted faces it has. Corner cubes get 3 painted faces, edge cubes get 2, face-center cubes get 1, and inner cubes get 0. This follows a fixed pattern based on the number of cuts.

• If a cube is cut into n x n x n smaller cubes (n cuts per side means n+1 pieces — be careful, usually the problem says cut into n equal pieces per side meaning n slices total)
• 3 painted faces: always 8 (the 8 corner pieces, regardless of n)
• 2 painted faces: 12 x (n-2) where n is number of smaller cubes per edge
• 1 painted face: 6 x (n-2) squared
• 0 painted faces: (n-2) cubed
• Total small cubes = n cubed, verify by adding all four categories

Unfolded Cube or Net of a Cube

AFCAT sometimes shows an unfolded cube (a net) and asks which faces are opposite or which folded shape is correct. There are 11 valid nets of a cube. You do not need to memorize all 11. The practical trick is to identify which faces share an edge and which faces are separated by 2 or more steps — separated faces by 2 steps in a straight line are always opposite.

• In a straight row of 4 squares in a net, the 1st and 4th are always opposite faces
• In a cross-shaped net, the center and the face directly above or below it across a gap are opposite
• Faces that are corner-to-corner (diagonal) in the net are never opposite
• Fold the net mentally step by step — fold bottom up, then sides in
• Practice the T-shape and L-shape nets as they appear most in AFCAT

• Applying the 1-6, 2-5, 3-4 rule to non-standard dice — the question may clearly show a non-standard arrangement so always check the given diagrams first
• Confusing n as number of cuts versus number of pieces — if a cube is cut into 3 equal parts along each edge, n = 3 pieces (not 3 cuts), so use n = 3 in formulas
• Thinking corner cubes change with different sizes — they are ALWAYS 8, not more, not less
• In net problems, marking adjacent faces in the unfolded diagram as opposite — adjacent in the net means they share an edge when folded, so they are never opposite
• Rushing dice rotation questions by guessing — always anchor one common face between two views before deciding orientation

• SEVEN RULE for standard dice: Any two opposite faces sum to 7. Memorize as S-E-V-E-N = Six Equals Very Exact Number (1+6, 2+5, 3+4).
• CEF-I for painted cubes: Corners=8, Edges=12(n-2), Faces=6(n-2)^2, Inner=(n-2)^3. Remember the word CEFI like a filing system.
• For nets: ROW OF FOUR, first and last are a pair — like the first and last person in a queue sitting opposite each other at a round table.
• Dice rotation trick: Think of a dice like a compass. Fix North face, then East, South, West rotate in sequence. Never let two visible faces in one view be called opposite.

• AFCAT typically places 2 to 3 dice questions and 1 to 2 cube-painting questions in the Military Aptitude section. Budget 30 to 45 seconds per dice question and about 60 seconds for cube-painting.
• Dice questions in recent AFCAT papers mostly give 2 positions of the same dice and ask for the opposite or bottom face — the anchor method solves these in under 20 seconds.
• Cube-painting questions almost always use n = 3 (27 cubes) or n = 4 (64 cubes). Memorizing the answers for these two cases saves time: for n=3 the split is 8-12-6-1 and for n=4 it is 8-24-24-8.
• Watch for the phrase differently colored faces or only some faces painted — if only 4 or 5 faces are painted, the corner and edge formulas change. Read the question carefully before applying standard formulas.
• In AFCAT Military Aptitude, difficulty is low to moderate. These questions are scoring if you know the rules cold. Never skip them — they are among the fastest marks available in the section.