Question 84
A midpoint plotter is an instrument that draws the exact midpoint of two previously marked points. Starting from two points at distance $1$ and using only the midpoint plotter, you must obtain two points at a distance strictly between $\frac{1}{2017}$ and $\frac{1}{2016}$, drawing the smallest possible number of points. What is the minimum number of times you need to use the midpoint plotter, and what strategy would you follow to achieve your goal?