Prove this logically

I just now went for my walk and I guess it cleared away a few cobwebs.


When you take away the 4 bowls, imagine that they become "invisible bowls" to be used only when more than one ball is placed in any standard bowl. Now whenever you place an extra ball in a bowl, it resides inside one of the "invisible bowls." Thus you still have 14 slots in which to place the 5 balls in. Also, to illusrate this more clearly, since the bowls are each numbered, let's leave their respective numbers on the "invisible bowls." Now nothing has really changed.


Is it a proof? I doubt it, but it shows how it works.