4
Problems(2)
n numbers around the circle
Source: 239 2008 S4
7/28/2020
For what natural number can pairwise distinct numbers be arranged on a circle such that each number is either greater than numbers following it clockwise or less than all of them? and would any property be violated when deleting any of those numbers?
combinatorics
Inscribed hexagon
Source: 239 2008 J4
7/28/2020
Point is located inside an acute-angled triangle . , , are points symmetric to with respect to the sides of triangle . It turned out that the hexagon is inscribed. Prove that is the Torricelli point of triangle .
geometry