Question

q 28 please answer soon......
only answer if u know
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Answer 1

Answer:

B) 8

Step-by-step explanation:

Consider one of the corners of the die in the middle.

There are 8 dice meeting at this corner, so there must be at least 8 different colours.

To show that 8 is the answer, we just need to show that it is possible to do it with as few as 8 colours.

Divide the cubes into sets as follows:

1 set of size 1:   the middle die

3 sets of size 2:  pairs of dice in the middle of opposite faces

3 sets of size 4:  four edge dice in a plane that cuts the cube in half

1 set of size 8: the 8 corner dice

Notice this accounts for all 1×1 + 3×2 + 3×4 + 1×8 = 1+6+12+8 = 27 dice.

Also, no two dice in the same set meet at a corner, so the dice in a common set can safely be assigned the same colour.

The number of sets is 1 + 3 + 3 + 1 = 8.

So with 8 colours, we can assign a colour to each set and this achieves the required result.