Day 6

This question is just a math problem.

Let \(h\) be how much time you hold the button and \(T\) be the total time you have. Then, since you leave at \(h\) speed, you walk for \(h\cdot (T-h)\) units of distance.

Now, for each pair \((T, d)\), you would need to find all values of \(t\) such that \(t \cdot (T-t) > d\).

If we want to just count (which is more than enough for the problem), we just need to filter in the range of \(0..T\) for those values and then count them.

However, the result can also be calculated explicitly. For that, we just need to find the values of \(t_1, t_2\) for which \(t \cdot (T-t) = d\), i.e. \(t \cdot (T-t) - d = 0\) and then the range will be the integral values that are between \(t_1\) and \(t_2\).