MathDB

The points

A_1,A_2, \ldots , A_{1983}

are set on the circumference of a circle and each is given one of the values

\pm 1

. Show that if the number of points with the value

+1

is greater than

1789

, then at least

1207

of the points will have the property that the partial sums that can be formed by taking the numbers from them to any other point, in either direction, are strictly positive.

Problem Statement