Six letters P, J, U, W, L and K are written on different faces of a dice. Two positions of this dice are shown in the figures below. Find the letter on the face opposite to P.

Correct — B. Two views are drawn. In the first, P is on top with J on the left face and U on the right.
In the second, W is on top with J again on the left face and L on the right.

Rule: two faces drawn in the same picture share an edge, so neither can be opposite the other.

J holds the left face in both views, so the die was turned about the axis running through J and the face behind it. J is drawn beside P, U, W and L, which leaves K as the face opposite J.

That makes P, U, W and L a ring of four round the J–K axis. A quarter-turn about that axis would bring P to the right face or U to the top, and the second view shows L and W there instead.

So the turn is a half-turn, which swaps top with bottom. W arrives on top, so W was the bottom face while P was on top: P is opposite W → option (b).

Why the others are wrong

• (a)
  K — K is the one letter that never appears. It is opposite J, the face that keeps its place across both views, not opposite P.
• (c)
  U — U is drawn on the right face while P is on top in the first view. Faces shown together share an edge and cannot be opposite.
• (d)
  J — J stands beside P in the first view, so it touches P. J is the face the die turns about, and its opposite is K.

A die has three opposite pairs. Every face you can see in one drawing touches the other two you can see, so each picture rules out three pairings at once.

When a letter appears in both views, it is doing double duty: it tells you which faces touch it, and it tells you the axis the die was turned about. Both facts are needed here, because adjacency alone only settles K.

Key facts

• Faces visible in the same drawing are adjacent, never opposite.
• J occupies the left face in both views, so P, U, W and L all touch it and K is opposite J.
• A half-turn about the J–K axis swaps the top face with the bottom face.
• The six letters here are P, J, U, W, L and K.

Common traps

• Naming the unseen letter out of habit — here K is opposite J, not P.
• Assuming the two views differ by a quarter-turn without testing it.
• Treating the left and right faces as a fixed pair when only the left one repeats.

No directly related past PYQ was found.