Six words ‘Eat’, ‘Play’, ‘Cry’, ‘Sleep’, ‘Dance’ and ‘Run’ are written on different faces of a dice. Two positions of this dice are shown in the figure below. Find the word on the face opposite to ‘Eat’.

Correct — B. View 1 shows Eat on top, Cry on the left face and Play on the right. View 2 shows Play on top, Cry on the left and Dance on the right.

Rule: Cry holds its face, so the die has turned about the Cry axis, and the other four faces ride one ring: right → top → back → bottom → right.

Play went right → top. Under the same turn the old bottom face comes up to the right, and that face reads Dance.

So Dance was the hidden bottom in view 1, under Eat. Top and bottom are opposite, so Eat is opposite Dance → option (b).

Why the others are wrong

• (a)
  Sleep — Sleep appears in neither drawing, so nothing in the figure places it at all. The two views already fix Eat's opposite face as Dance.
• (c)
  Play — Play and Eat are visible together in view 1. Two faces drawn in one view meet along an edge, so they are adjacent and can never be opposite.
• (d)
  Cry — Cry is visible together with Eat in view 1, which makes the two adjacent. Cry is in fact the axis face the die was turned about.

A dice item hands you two or three views and asks for one hidden relationship. Two rules do nearly all the work.

First, any two faces drawn in the same view are adjacent, never opposite. The picture shows three faces meeting at a corner, so the left and right faces of the drawing touch each other.

Second, when one face repeats in the same position across two views, the die has been rotated about that face and the remaining four move round it in a ring. Track one face's move to fix the direction of the turn, then read everything else off the ring.

Key facts

• View 1 shows Eat on top with Cry and Play on the side faces.
• View 2 shows Play on top with Cry and Dance on the side faces.
• Cry occupies the same face in both views, which makes it the axis of the rotation.
• Faces drawn in the same view are adjacent, so Eat cannot be opposite Play or Cry.

Common traps

• Treating the left and right faces of the drawing as opposite, when the drawing shows three faces meeting at a corner.
• Concluding that Sleep must be opposite Eat merely because it is missing from both views.
• Reading the two pictures as two different dice rather than one die turned.

No directly related past PYQ was found.