Six numbers 21, 22, 23, 24, 25 and 26 are written on different faces of a…

When analyzing multiple positions of a dice, faces that appear together are adjacent to one another and cannot be opposite.

Analyze Positions:

Position 1: Faces 21, 23, and 25 are visible. (21 is adjacent to 23 and 25; 23 is adjacent to 25).

Position 2: Faces 21, 25, and 22 are visible. (21 is adjacent to 25 and 22; 25 is adjacent to 22).

Position 3: Faces 25, 24, and 22 are visible. (25 is adjacent to 24 and 22; 24 is adjacent to 22).

Determine Opposites:

From Positions 2 and 3, we see that 25 and 22 are adjacent to both 21 (Position 2) and 24 (Position 3).

Looking at Position 3, the faces visible are 25, 24, and 22.

Looking at Position 2, the faces visible are 21, 25, and 22.

If we compare the common faces between Position 2 and 3 (which are 25 and 22), we can deduce the orientation. However, a simpler way is to look at all numbers: 21, 22, 23, 24, 25, 26.

In Position 3, 24 is adjacent to 25 and 22.

In Position 1, 25 is adjacent to 21 and 23.

By comparing the faces adjacent to 25 across all views, we see it is adjacent to 21, 22, 23, and 24. The only remaining number is 26, meaning 25 is opposite to 26.

Now, looking at Position 3 again, 24 is adjacent to 25 and 22. We know from the other positions that 21 is adjacent to 25 and 22 as well. This implies that 24 is opposite to 21.