15

Part of 2021 Baltic Way

Problems(1)

Wild combo geo appeared!

Source: Baltic Way 2021, Problem 15

For which positive integers

n\geq4

does there exist a convex

n

-gon with side lengths

1, 2, \dots, n

(in some order) and with all of its sides tangent to the same circle?

geometrycombinatorial geometrygeometry proposedcombinatoricscombinatorics proposed