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Omni-MATH / In the city of Flensburg there is a single, infinitely long, street with…

Problem

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problem

In the city of Flensburg there is a single, infinitely long, street with housesnumbered 2,3,…2, 3, \ldots. The police in Flensburg is trying to catch a thief who every night moves from the house where she is currently hiding to one of its neighbouring houses. To taunt the local law enforcement the thief reveals every morning the highest prime divisor of the number of the house she has moved to. Every Sunday afternoon the police searches a single house, and they catch the thief if they search the house she is currently occupying. Does the police have a strategy to catch the thief in finite time?
Plain-text mathematical notation (without MathML)
In the city of Flensburg there is a single, infinitely long, street with housesnumbered 2,3,…. The police in Flensburg is trying to catch a thief who every night moves from the house where she is currently hiding to one of its neighbouring houses.

To taunt the local law enforcement the thief reveals every morning the highest prime divisor of the number of the house she has moved to.

Every Sunday afternoon the police searches a single house, and they catch the thief if they search the house she is currently occupying. Does the police have a strategy to catch the thief in finite time?
Original LaTeX notation
In the city of Flensburg there is a single, infinitely long, street with housesnumbered $2, 3, \ldots$. The police in Flensburg is trying to catch a thief who every night moves from the house where she is currently hiding to one of its neighbouring houses.

To taunt the local law enforcement the thief reveals every morning the highest prime divisor of the number of the house she has moved to.

Every Sunday afternoon the police searches a single house, and they catch the thief if they search the house she is currently occupying. Does the police have a strategy to catch the thief in finite time?

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Source and history

task_id
2afa8107-e69d-5e40-b3c7-47d3b8602421
task_key
test--2afa8107-e69d-5e40-b3c7-47d3b8602421
task_revision_id
1
config / split
/ test

Official source

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