i got this problem that we need to prove that we cannot pick 28 points that are 1.75cm(atleast) from eachother in a cube where each edge is 3cm long .
i tried $dividing$ each square in the cube to $4$ , that way we will get that each edge is $1.5cm$ now and the hypotenuse will be $2.12$ $\left(\frac{3\sqrt 2}{2}\right)$ i did this because i think its the smallest distance we can get
now since a cube has 6 squares , and my squares are divided to have 4 smaller cubes in each one we get $4*6=24$ which leaves us 4 extra points which means some squares will have $2$ points in them but i cannot tell if i did right or even close to it because of the information in the question (atleast 1.75 distance between each point)
i tried to demonstrate what i meant 
thanks to any helpers , and sorry if there are translation mistakes
The hint is the number 28, which is one more than 27, which is $3^3$
Hint: Divide the cube into 27 smaller cubes of side length $1$ cm.