Problem 1

Part of 1999 VJIMC

Problems(2)

infinite product of k/(k+∞)

Source: VJIMC 1999 1.1

\lim_{n\to\infty}\left(\prod_{k=1}^n\frac k{k+n}\right)^{e^{\frac{1999}n}-1}.

limitsreal analysis

set of k lines has 3 skew or 3 concurrent

Source: VJIMC 1999 2.1

Find the minimal

k

such that every set of

k

different lines in

\mathbb R^3

contains either

3

mutually parallel lines or

3

mutually intersecting lines or

3

mutually skew lines.

geometrycombinatoricscombinatorial geometry3D geometry