maths and logic

[paperback]

a cube is made of chocolate the outside covered in white icing if the cube is cut into 125 smaller cubes of exactly the same size how many sides will have at least 2 sides with white icing many thanks

[kosoro]

44???

[Gnu]

Which cubes have 3 sides coated with icing? How many of these are there?

Then imagine which cubes have 2 sides coated in icing, remembering not to include the ones with 3 sides coated. Where are they on the cube, and how many of these are there?

[soliloquy]

56?

[Dinkypuzzled]

32

[soliloquy]

On a recount - 44

[Dinkypuzzled]

The large cube is 5x5x5 larger than the smaller cubes.

Each face has 16 round the edge with at least 2 sides iced. 8 faces - but don't count any twice - 32

[Dinkypuzzled]

Oops - you're right, Soliloquy.

[Dinkypuzzled]

I should never have doubted Kosoro!

[Bob A Job]

What flavour is the icing? (not every icing goes with chocolate after all)

[Dinkypuzzled]

Come to think of it, not all the cubes would be exactly the same size. I'd like a corner one.(more icing.)

[BriWrite]

I made it =

27 pieces with no chocolate (The inside ones)

54 pieces with one side coated.

36 pieces with two sides coated.

8 pieces with three sides coated.

Confirming 36 + 8 = 44

[Salty]

The cube has 8 corners (each with 3 sides of icing), and 12 edges, each with 3 two-sided iced bits between the corners. Therefore total is 8 + 12x3 = 44.