As per the given diagram in above question , we can see that
The central cube of each face will have only one face painted.
Thus, there are <>six such cubes.
As per the given open dice in above question , we can see that
? lies opposite ?.
? lies opposite ?.
? lies opposite ?.
As per the given pattern in question figure , we can find the similar next position of given dice .
Red, Blue, Green and Orange colors are on the faces adjacent to Purple color.
Therefore, yellow color is opposite to purple color.
On the basis of following pattern in given dices , we can say that
Red, Blue, Yellow and White colors are on the adjacent faces of Green color. Therefore, Orange lies opposite Green color.
On the basis of following pattern in given dices , we can say that
Red, Orange, Yellow and Green colours are on the faces adjacent to white colour. Therefore, Blue colour lies opposite white colour.
We follow the given pattern :-
Yellow, Green, Red and Blue colours are on the faces adjacent to Purple.
So, Orange colour is opposite to Purple.
Total cubes 25
One column with 10 boxes = 1 × 10 = 10
Two column with 7 boxes = 2 × 7 = 14
One column with 4 boxes= 1 × 4 = 4
Total boxes = 28
Total cubes = 9
There are 9 columns with 5 cubes = 9 × 5
There are 7 columns with 4 cubes = 7 × 4
There are 5 columns with 3 cubes = 5 × 3
There are 3 columns with 2 cubes = 3 × 2
There is one column with 1 cubes = 1 × 1
Total = 9 × 5 + 7 × 4 + 5 × 3 + 3 × 2 + 1 × 1 = 81
Number 1 is common to both the figures (i) and (ii). The dice in fig. (ii) is assumed to be rotated so that 1 dot moves to the top face i.e to the same position as in figure (i) and 2 and 4 dots move to the face behind the faces with 3 and 5 dots respectively. Clearly by combination, 3 dots lie on the face opposite the face having 2 dots. Therefore, when there are 2 dots at the bottom, the number of dots at the top will be 3.
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