It is easy to coordinate the climbers' movement between the peaks and valleys
(local maxima and minima of the functions).
The difficulty is that to progress, the climbers must occasionally go down the mountain,
either one or the other, or both climbers.
Similarly, either one or the other climber must backtrack towards the beginning of the journey.
In fact, it has been observed that for a mountain with n peaks and valleys the number of turns
can be as large as quadratic in n.[1]
These complications make the problem unintuitive and sometimes rather difficult,
both in theory and in practice.
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