Two different positions of the same dice with faces K, B, V, M, P and T are shown below. Select the letter that will be on the face opposite to the one having B.

- (a)M
- (b)V
- (c)K
- (d)P
Answer
Why
Correct — A. K is on top in both views, so the cube has only been turned about its vertical axis and the four side faces keep their order round it.
Rule: read the same way round, B then V in view 1 must sit in the same loop as M then P in view 2.
The loop B, V, M, P satisfies both: start at M and it reads M, P, B, V, which is view 2. The alternative B, V, P, M never puts M immediately before P.
In a four-face loop the 1st is opposite the 3rd, so B is opposite M — option (a).
Why the others are wrong
- (b)V — V is drawn beside B on the same cube, so the two faces share an edge. Faces you can see together are adjacent and can never be opposite.
- (c)K — K is the face-up letter in both pictures, so it touches all four side faces including B. A top face is adjacent to every side face, not opposite one.
- (d)P — P is the fourth place in the loop and B the first, which makes them neighbours. The opposite face has to be two steps round, and that is M.
Concept
Two views showing the same letter in the same position are the quickest dice items to settle. K sits on top in both pictures, which fixes the change as a rotation about the vertical axis.
Such a rotation leaves the top and bottom faces where they are and slides the four side faces round. It cannot change their cyclic order.
So the pair visible in view 1, read left face then right face, and the pair in view 2, read the same way, must be consecutive in one loop of four.
That loop uses B, V, M and P. The sixth letter, T, appears in neither picture, which places it opposite K.
Only one of the two candidate loops survives. Test both orders rather than assuming the first one you write down, because the wrong loop pairs B with V and looks just as tidy.
Key facts
- K appears on top in both views, so view 2 is view 1 rotated about the vertical axis.
- A rotation about the vertical axis preserves the cyclic order of the four side faces.
- The side faces in order are B, V, M, P, which pairs B with M and V with P.
- T is shown in neither view, so T is the face opposite K.
Study next
Common traps
- Pairing the two letters that merely look far apart on the page
- Forgetting that B and V are adjacent because they are drawn side by side
- Assuming the letter missing from both views is opposite B rather than opposite the repeated face
The same two-position lettered-dice frame is asked at 12 Sep 2024, 09:00, Reasoning Q.18 (faces T, O, B, L, Y, V) and at 11 Sep 2024, 16:00, Reasoning Q.2 (faces R, P, T, S, M, B), both naming a letter and asking for its opposite.
Related PYQs
No directly related past PYQ was found.