### Archive

Archive for April, 2011

## El País’ weekly challenge

Consider a clock, with its twelve numbers around a circle: $1, 2, \dotsc, 12.$ Color each of the twelve numbers in either blue or red, in such a way that there are exactly six in red, and six in blue. Proof that, independently of the order chosen to color the numbers, there always exists a line that divides the circle in two perfect halves, and on each half there will be exactly three numbers in red, and three numbers in blue.