Six letters K, L, M, N, O and P are written on different faces of a dice. Three positions of this dice are shown in the figure. Find the letter on the face opposite to M.

Correct — D. Three views are drawn, and every face visible in one view is adjacent to the other two in that view.

View 1 shows M, K and O together.
View 2 shows O, K and N together.
View 3 shows K, L and N together.

Rule: a face is opposite the one letter it is never seen beside.

K appears with M, O, N and L — four faces — so K is opposite P, the only letter left.

P is therefore adjacent to everything except K. O is drawn with M, K and N, and is adjacent to P as well, which gives O its four neighbours and fixes O opposite L.

Two pairs are settled, K–P and O–L. Only M and N remain, so M is opposite N — option (d).

Why the others are wrong

• (a)
  K — Option (a) fails on view 1 alone — M and K are drawn on the same cube, so they are adjacent faces and cannot be opposite each other.
• (b)
  P — Option (b) puts P opposite M, but P is already spoken for: it is opposite K, because K is seen beside all four of M, O, N and L.
• (c)
  L — Option (c) is the tempting one, since L never appears beside M. But L is opposite O, once O is shown adjacent to M, K, N and, through the K–P pairing, to P.

A dice diagram gives you adjacency directly and opposition never. Two faces drawn in the same view are adjacent, and the face you want is the one letter that never shares a view with the target.

Six faces make three opposite pairs. Fix one pair and the problem shrinks, because the face opposite X becomes adjacent to all four remaining faces automatically.

That is the whole method here. K adjacent to four letters fixes K–P, P's forced adjacencies then fix O–L, and M–N falls out with no rotation at all.

Key facts

• Faces shown in the same view of a dice are adjacent, never opposite.
• K is seen beside M, O, N and L across the three views, which leaves P as the face opposite K.
• The three opposite pairs on this dice are K with P, O with L, and M with N.

Common traps

• Calling two faces opposite merely because they never appear together, without checking the alternative pair is already taken
• Working from two of the three views, which leaves the dice undetermined
• Rotating the cube mentally when plain adjacency counting settles it

No directly related past PYQ was found.