My english fails me here as I don't know how better to call it then whats in the title.
Basically the boxes have ranges like this
[1] [2-3] [4-6] [7-10] and so on with each box being 1 unit bigger then the last one.
Then I have a number, say 4. I need to find out mathematically which box its in (in this instance its in box 3). How could I do that?
Also I have no idea how to tag this.
Assuming your last box should be $[7-10]$, the upper limits of your boxes are the triangular numbers. To find which box a number $x$ is in, compute $n=\frac 12(\sqrt {1+8x}-1)$ as shown in Wikipedia and round up