MathDB

On the table there are written numbers

673, 674, \cdots, 2018, 2019.

Nibab chooses arbitrarily three numbers

a,b

and

c

, erases them and writes the number

\frac{\min(a,b,c)}{3}

, then he continues in an analogous way. After Nibab performed this operation

673

times, on the table remained a single number

k

. Prove that

k\in(0,1).

Problem Statement