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SSC CGL Reasoning · Dice and Cubes

Turning About a Common Face

When two views of a dice show the same face in the same place, the dice has turned about that face, so the faces sitting in matching places in the two views are opposite each other.

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Why this matters

Twenty-two questions in the bank, 4 from the 2023 shifts and 18 from the 2024 shifts, with 4 EASY and 18 MODERATE. The neighbour rule alone often cannot reach the face asked for here; the common-face rule gives every opposite pair in one step.

Concept 1 of 1: Faces in matching places are opposite

If a face stays in the same place in two views, the dice has only turned round it. The four faces around it keep their order, so each face in the first view has been replaced, in the same spot, by the face opposite it.

Definition

1. Find the face shown in both views. 2. Check that it sits in the same place in both (both on top, or both on the right). 3. Pair the other faces by position: the first view's top with the second view's top, its left with the second's left. Each pair is opposite. 4. The common face is opposite the one face that appears in neither view.

  • If the common face is in different places, the rule does not apply directly; use the neighbour rule, or go round the common face in the same direction in both views.
  • Fast route: with the common face in the same place, read the answer straight off the matching position.

Worked example

Two views of a dice: (top 4, left 1, right 2) and (top 6, left 1, right 3). Which number is opposite 4?
Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 26 Sep 2024, Shift 2 · Q8Moderate

Example 1 · Dice and Cubes · Turning About a Common Face

Six numbers 5, 3, 6, 7, 9 and 2 are written on different faces of a dice. Two positions of this dice are shown in the figure below. Find the number on the face opposite to the one having 5.

Using the rule when the common face has moved

If the shared face is on top in one view and on the left in the other, matching positions do not pair opposite faces. Check that the common face is in the same place first.

Pairing the common face with a shown face

The common face is opposite the face that appears in neither view, not any face shown beside it. Every face shown with it is a neighbour.

Matching a top with a front

Pair the faces by exactly the same position: top with top, left with left. Pairing the first view's top with the second view's front gives a wrong pair.
Drill 21 more on faces in matching places are opposite

Summary — formulas & gotchas at a glance

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Test yourself on Dice and Cubes

20 past SSC CGL questions from this chapter, timed at 12 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

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