MathDB

In the night, stars in the sky are seen in different time intervals. Suppose for every

k

stars (

k>1

), at least

2

of them can be seen in one moment. Prove that we can photograph

k-1

pictures from the sky such that each of the mentioned stars is seen in at least one of the pictures. (The number of stars is finite. Define the moments that the

n^{th}

star is seen as

[a_n,b_n]

that

a_n<b_n

Problem Statement