Question 9
Two thousand points are given on a circle. Label one of the points $1.$ From this point, count $2$ points in the clockwise direction and label this point $2.$ From the point labeled $2,$ count $3$ points in the clockwise direction and label this point $3.$ (See figure.) Continue this process until the labels $1,$ $2,$ $3,$ $\ldots,$ $1993$ are all used. Some of the points on the circle will have more than one label and some points will not have a label. What is the smallest integer that labels the same point as $1993?$
