Question 6
Two mathematicians, lost in Berlin, arrived on the corner of Barbarossa street with Martin Luther street and need to arrive on the corner of Meininger street with Martin Luther street. Unfortunately they don't know which direction to go along Martin Luther Street to reach Meininger Street nor how far it is, so they must go forwards and backwards along Martin Luther street until they arrive at their destination. What is the smallest value for a positive integer $K$ so that they can be sure that if there are $N$ blocks between Barbarossa street and Meininger street then they can arrive at their destination by walking no more than $KN$ blocks (no matter what $N$ turns out to be)? The mathematicians always walk together.