IMO Shortlist 1971 problem 14
Dodao/la:
arhiva2. travnja 2012. A broken line
![A_1A_2 \ldots A_n](/media/m/3/d/b/3dbfe0f5b1f84bfc9be4ee4d64979438.png)
is drawn in a
![50 \times 50](/media/m/3/c/7/3c74bd2c89e72fceccea7c3c46aec21c.png)
square, so that the distance from any point of the square to the broken line is less than
![1](/media/m/a/9/1/a913f49384c0227c8ea296a725bfc987.png)
. Prove that its total length is greater than
%V0
A broken line $A_1A_2 \ldots A_n$ is drawn in a $50 \times 50$ square, so that the distance from any point of the square to the broken line is less than $1$. Prove that its total length is greater than $1248.$
Izvor: Međunarodna matematička olimpijada, shortlist 1971