Hello,

This schoolyear I started the study Mathematics. One of my first subjects is Calculus. I can earn extra points for my exam when I do my homework well. Ofcourse I'll take my opportunity and do as much homework as possible to pass my first year.

The question:
There's a chocolate bar, existed of n amounts pieces. Where n is a natural number (1, 2, 3, 4, ...). It's a rectangular bar that I have to break along the sides. I have to break it till I own n single pieces. Now: show that I have to break the chocolate bar (atleast) n-1 times.

Can someone help me with this problem, please?

Question

Hello,

This schoolyear I started the study Mathematics. One of my first subjects is Calculus. I can earn extra points for my exam when I do my homework well. Ofcourse I'll take my opportunity and do as much homework as possible to pass my first year.

The question:
There's a chocolate bar, existed of n amounts pieces. Where n is a natural number (1, 2, 3, 4, ...). It's a rectangular bar that I have to break along the sides. I have to break it till I own n single pieces. Now: show that I have to break the chocolate bar (atleast) n-1 times.

Can someone help me with this problem, please?

parthkohli · Answer

Let's say that the number of cuts is a function of the number of pieces.$$f(1) = 2$$means that for 1 cut, we have 2 pieces.$$f(1) = 2\f(2) = 3\f(3) = 4\\vdots \quad \quad \vdots \f(n - 1) = n$$

parthkohli · Answer

You can visualize it by drawing.|dw:1347141343345:dw|

anonymous · Answer

Ah yes I see! Thank you a lot ParthKohli. The only problem I stuck with now, is that we probably have to determine the inductionstep. This is the very logical way, but the way to note is a bit different. Anyways, many thanks for your help!