Another proof by strong induction problem I am trying to solve the following problem using proof by strong induction. the problem is:
Assume that a chocolate bar consists of n squares arranged in a rectangular pattern. The entire bar, or any smaller rectangular piece of the bar, can be broken along a vertical or a horizontal line separating the squares. Assuming that only one piece can be broken at a time, determine how many breaks you must successively make to break the bar into n separate squares
The farthest i have gotten is the basis step, but i dont even know if that is correct
Potential basis step that i got it is P(n), but besides that i am clueless
 A: We prove that a rectangular bar with $n$ squares always requires $n-1$ breaks.  
Recall that a "break" divides a rectangle into two rectangles along score lines. 
For the induction step, suppose that for all $m\lt n$, a bar with $m$ squares requires $m-1$ breaks.  We show that a bar with $n$ squares requires $n-1$ breaks. 
Break the $n$-bar into two rectangles, say of size $a$ and $b$, where $a+b=n$ and $a\lt n$, $b\lt n$.
The breaking used $1$ break. By the induction assumption, dissecting the $a$-rectangle into unit squares will use $a-1$ breaks, and the $b$-rectangle will use $b-1$ breaks, for a total of $1+(a-1)+(b-1)=n-1$. 
A: I know that this is not a proof by induction but it really is a nice solution to the problem. 
Suppose the bar consists of n pieces. We know that every cut always divides a large rectangle into two smaller pieces, thus creating exactly one new piece with every cut. Since we start with 1 big bar and we want n pieces, we have to break the bar exactly n-1 times.
A: For n=1, we need 0 break.
For n=2, we need 1 break.
For n=3, we need 2 breaks.
So say for n=j, its true and we need j-1 breaks and its true for 
all j>0&& j<=k.
So a bar of k+1 squares can be broken down to 2 rectangles 
with squares < k , which is already true.
Hence proved.
