deletions | additions       diff --git a/3.tex b/3.tex  index 0be6795..41b03bb 100644  --- a/3.tex  +++ b/3.tex 
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That looks good. At about 2km, scores start to get quite low (25) and by $\sim$4km the user will get almost no points. That's pretty reasonable for a city the size of Belo Horizonte, but if you take a really small city, getting 25 points for a 2km distance might be just too much. So let's adjust the score based on the size of the city.   Suppose $A_{\mbox{bh}}$ is Belo Horizonte's area, we can create a coefficient $\alpha=A_{\mbox{city}}/A_{\mbox{bh}}$. As the value of $\alpha$ increases, more decreases, less  points should be awarded to the user. So, the same way we did for easiness, we also divide $d$ by this coefficient, but since it represents an area (which follows the \href{https://en.wikipedia.org/wiki/Square-cube_law}{square cube law}), we take it's square root first. Which leads us to: \begin{equation}  S = \frac{100}{1 + \left(\frac{d}{e\sqrt{\alpha}}\right)^4}