Why Do Three Blocks on a Frictionless Surface Accelerate at the Same Rate?

[astrololo]

Homework Statement

On a surface without friction, we have 3 blocs with mass A=0,4 kg B=0,1 Kg C=0,3 Kg which are placed one beside the other, with A being first, B second and C third.. If we push on the bloc A with a horizontal force of 2,4 N, determine what is the acceleration and what are the forces of the normals which are located between the blocs.

http://imgur.com/F9PQwKK

Homework Equations

Sum force of x = m * a(x)

The Attempt at a Solution

I was able to resolve the problem and got the right answers. What I was wondering is why should I assume that the acceleration is going to be the same for the 3 blocs ? I was able to solve the problem because I assumed this to be true, but I don't know why it is. I guess that the fact there's no friction makes this true. any help ?

 

[BvU]

Well, given the picture, B and C can't accelerate slower than A. There also is nothing that could make them accelerate faster.

Does that answer your question ?

 

[astrololo]

Well, given the picture, B and C can't accelerate slower than A. There also is nothing that could make them accelerate faster.

Does that answer your question ?

Said this way, it makes sense. Ty