In the closed interval [0, 1] there are 999 equally spaced red dots and 1,110 equally spaced blue dots (not on the endpoints). Thus the red dots divide the interval into 1,000 subintervals and the blue dots divide the interval into 1,111 subintervals. What is the smallest distance beween any two points within this interval and how many pairs $(r_i, b_k)$ exist, i.e. pairs in which a red dot is followed by a blue dot?
My tentative thoughts (that didn´t get me any further): Draw a square $ABCD$ with coordinates $A(0, 0), B(0,1), C(1,1)$ and $D(0,1)$ into a cartesian coordinate system. Draw a grid (wlog) with 1,110 parallel lines to the x-axis and 999 lines parallel to the y-axis. The diagonal $y = x$ intersects the grid lines at $(x_i, y_j)$ and the minimum distance to the grid line ist he solution. How can I solve this?