Question 85
In the land of Flensburg there is a single, infinitely long, street with houses numbered $2, 3, \ldots$ The police in Flensburg is trying to catch a thief which every day moves from the house where he is currently hiding to one of its neighbouring houses.
To taunt the local law enforcement the thief reveals every day the highest prime divisor of the house he will move to.
Every Sunday the police are allowed to search a single house, and they catch the thief if they search the house he is currently occupying. Determine if the thief will be able to escape the police indefinitely or if the police has a strategy to catch the thief in finite time.
To taunt the local law enforcement the thief reveals every day the highest prime divisor of the house he will move to.
Every Sunday the police are allowed to search a single house, and they catch the thief if they search the house he is currently occupying. Determine if the thief will be able to escape the police indefinitely or if the police has a strategy to catch the thief in finite time.