Hello cadets!
A robber is on the loose. Today’s puzzle is to locate them. In the robber’s favour, they can run faster than any police officer, but in the force’s favour, it has at its disposal an infinite number of officers.
Police chase
The streets of a city are a square grid that extends infinitely in all directions. One of the streets, Broadway, has a police officer stationed every 100 blocks.
A robber is somewhere in the city.
Can you devise a strategy that guarantees the criminal will be spotted by the police at some point in time?
Relevant information: The robber and the police officers are in a street at all times. The robber has a finite maximum running speed, which is faster than any officer’s. The police can see infinitely far.
I’ll be back at 5pm UK with the solution.
UPDATE: Read the solution here.
Meanwhile, I would like to remind you of your rights as a reader of this column. You are not obliged to say anything, but if you do write anything below the line PLEASE NO SPOILERS or it will definitely be used as evidence against you.
Instead discuss your favourite 1980s goofball comedies, or favourite police chases.
Thanks to Professor Alex Lvovsky of the University of Oxford for this puzzle. Prof Lvovsky is the head of COMPOS, an online program that gives free tuition in maths and physics for students in years 10, 11 and 12 (GCSE and A-level). The idea is to enable enthusiastic teenagers to learn these subjects at a deep level, with regular tiutorials by Oxford physics undergraduates and graduates. Registration for the next academic year is open now.
I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
I give school talks about maths and puzzles (online and in person). If your school (or police academy) is interested please get in touch.
