# How do you write a function rule for the number of cuts you need to make to cut a rope into x pieces?

Feb 2, 2015

Let's make some simple observations that will clear the general rule: with no cuts, you have the whole original rope, so we have that zero cuts $\setminus \rightarrow$ one piece.

If you cut the rope once, you will split it in two parts, so we have that one cut $\setminus \rightarrow$ two pieces.

I hope that it is clear by now that if you cut the rope $n$ times, you will split it into $n + 1$ pieces. So, the number of pieces is one more than the number of cuts.

If you want to see it the other way, you have that the number of cuts is one less than the number of pieces, so if you want $x$ pieces, you'll have to do $x - 1$ cuts.